Vector

Problem 101

The endpoints of AB\overline{A B} are A(3,4)A(-3,-4) and B(2,1)B(2,1). Point CC lies on AB\overline{A B} and is 15\frac{1}{5} of the way from AA to BB. What are the coordinates of point CC ? Explain how you found your answer.
Select the correct answer below and fill in the answer box to complete your answer. (Type an ordered pair.) A. First, find 15\frac{1}{5} of the horizontal and vertical distances from AA to BB. Then, move this amount from AA to CC. The coordinates of point CC are \square B. Use the Distance Formula to find 15\frac{1}{5} the length of AB\overline{\mathrm{AB}}. The coordinates of point C are \square c. First, find 15\frac{1}{5} of the horizontal and vertical distances from AA to BB. Then, move this amount from B to C. The coordinates of point C are \square \square 7. D. CC is the midpoint of AB\overline{A B}, so use the Midpoint Formula. The coordinates of point CC are \square .

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Problem 102

```latex \textbf{Forces in Two Dimensions} \\ \textbf{Name:} \\ Sencera Hariff \\
\textbf{Adding and Resolving Forces} \\ \text{Read from Lesson 3 of the Vectors and Motion in Two-Dimensions chapter at The Physics Classroom:} \\ \text{http://www.physicsclassroom.com/Class/vectors/u313a.html} \\ \text{http://www.physicsclassroom.com/Class/vectors/u313b.html} \\ \text{MOP Connection:} \\ \text{Forces in Two Dimensions: sublevels 1 (mostly) and 3 (a little)} \\
\textbf{Review:} \\
1. \text{Quantities fully described by magnitude alone are} \qquad ; \text{quantities that are described fully by both magnitude and direction are} \qquad \\

2. \text{Use a protractor to estimate the direction of the following vectors using the CCW notation.} \\
\text{Resultant:} \qquad \\ \text{Eq'n:} \qquad \text{Choose two. Be careful!} \\
\text{Resultant:} \qquad \\ \text{Eq'n:} \qquad \\
4. \text{A vector component} \qquad \\ \text{a. describes the effect of a vector in a given direction.} \\ \text{b. is found as the projection of a vector onto a coordinate axis.} \\
\textbf{Addition of Vectors and the Equilibrium Principle} \\
5. \text{When vectors are added using the head-to-tail method, the sum is known as the resultant. When force vectors are added, the sum or resultant is also known as the} \qquad \\ \text{a. scalar} \\ \text{b. average} \\ \text{c. equilibrant} \\ \text{d. net force} \\

6. \text{Several forces act upon an object. The vector sum of these forces ends up being 0 Newtons. The object is described as being} \qquad \\ \text{a. weightless} \\ \text{b. at equilibrium} \\ \text{c. stationary} \\ \text{d. disturbed} \\
7. \text{Which of the following is always true of an object that is at equilibrium? Select all that apply.} \\ \text{a. The net force acting upon it is 0 Newtons.} \\ \text{b. The individual forces acting upon it are balanced.} \\ \text{c. The object is at rest.} \\ \text{d. The object has no acceleration.} \\ \text{e. The object has a constant (unchanging) velocity.} \\
\text{(c) The Physics Classroom, 2020} \\ \text{Page 1} ```

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Problem 103

\begin{enumerate} \setcounter{enumi}{3} \item A vector component \_\_\_\_\_\_ Choose two. Be careful! \begin{enumerate} \item describes the effect of a vector in a given direction. \item is found as the projection of a vector onto a coordinate axis. \end{enumerate} \end{enumerate}

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Problem 104

W =3cm 0 =20w Magnitude, F Angle, = tan Forces in Two Dimensions Resolving Forces into Vector Components 8. Consider the vectors below. Determine the direction of the two components by circling two directions (E, W, N or S). Finally indicate which component (or effect) is greatest in magnitude. N N N W -E W -E W -E 9. S Components: E W N Greatest magnitude? S S S Components: EWNS Components: E W NS Greatest magnitude? Greatest magnitude? Each diagram displays a vector. The angle between the vector and the nearest coordinate axes is marked as theta (). If is gradually increased to 90 degrees, the magnitudes of the components would change. Which component would increase - horizontal (E/W) or vertical (N/S)? W N -E N E N E S S S Increasing component? Increasing component? Increasing component? E W N S E W N S E W N S
10. For the following situations, draw and label the force components of the given vector. Then use trigonometric functions to determine the magnitude of each component. Label the magnitudes of the component on the diagram. PSYW a. A 5.0 N force is exerted upon a dog chain at an angle of 65° above the horizontal. b. A baseball is hit by a bat with a force of 325 N at a direction of 105°. F © The Physics Classroom, 2020 Page 2

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Problem 105

Saudy A(0,0),B(6,1),C(2,6)A^{\prime}(0,0), B^{\prime}(-6,-1), C^{\prime}(-2,-6) 0), B(6,1)B(6,1), and coordinates A(0A(0,
A triangle has 0),B(6,1)0), B(6,1), and C(2,6)C(2,6). Find the coordinates of A,BA^{\prime}, B^{\prime}, and CC^{\prime} A(0,0),B(6,1),C(2,6)A^{\prime}(0,0), B^{\prime}(6,-1), C^{\prime}(2,-6) after a 180180^{\circ} rotation around Point AA. A(0,0),B(6,1),C(2,6)A^{\prime}(0,0), B^{\prime}(-6,1), C^{\prime}(-2,6) Back Nexps

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Problem 106

(1,0,,0)(1,0,1,0)(1,0,r)(1,0, \cdots, 0) \quad(1,0,1,0) \quad(1,0, r)

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Problem 107

For the following vectors, (a) find the dot product vw\mathbf{v} \cdot \mathbf{w}; (b) find the angle between v\mathbf{v} and w\mathbf{w}; (c) state whether the vectors are parallel, orthogonal, or neither. v=5i+3j,w=3i5j\mathbf{v}=5 \mathbf{i}+3 \mathbf{j}, \mathbf{w}=3 \mathbf{i}-5 \mathbf{j} (a) vw=v \cdot w= \square (Simplify your answer.)

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Problem 108

What are the coordinates of the point which is in the middle (midpoint) of the brown points? \square 1

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Problem 109

Translate the ghost 3 units up and 10 units left.

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Problem 110

An airplane flies 3333^{\circ} for 210 mi , and then 280280^{\circ} for 180 mi . How far is the airplane, then, from the starting point, and in what direction is the plane moving?
The airplane flies approximately \square { }^{\circ} for \square miles \square from the starting point. (Simplify your answers. Round to the nearest integer as needed.)

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Problem 111

/0.52 Points] DETAILS MY NOTES LARAT11 8.4.039.
Find the angle θ\theta (in degrees) between the vectors. (Round your answer to two decimal places.) u=3i+4jv=9i+7jθ=7.00\begin{array}{c} \mathbf{u}=3 \mathbf{i}+4 \mathbf{j} \\ \mathbf{v}=-9 \mathbf{i}+7 \mathbf{j} \\ \theta=7.00 \end{array} Need Help? Read It Submit Answer

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Problem 112

15.923 incorrect
The answer above is NOT correct.
Find the lengths of the three sides of the triangle ABCA B C in R3\mathbb{R}^{3} if A=(4,4,3),B=(5,4,3)A=(4,4,-3), B=(-5,4,3) and C=(1,1,2)C=(-1,-1,2). Enter your answers as a comma separated list. \square help (numbers)

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Problem 113

Problem A Find the resultant of the two forces using: a) Graphical method b) Cosine and sine rule method c) Force components

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Problem 114

Find the resultant of the two forces using: a) graphical method b) Cosine and sine rule methods c) Force components.

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Problem 115

что означает запись tundefined=xmundefined+ynundefined\overrightarrow{\mathrm{t}}=\mathrm{x} \overrightarrow{\mathrm{m}}+\mathrm{y} \overrightarrow{\mathrm{n}} ?
Выбери верный вариант ответа
Вектор tundefined\overrightarrow{\mathrm{t}} разложен по векторам mundefinedn\overrightarrow{\mathrm{m}} \overline{\mathrm{n}}
Вектор tundefined\overrightarrow{\mathrm{t}} разложен по векторам xundefinednyundefined\overrightarrow{\mathrm{x}} \mathrm{n} \overrightarrow{\mathrm{y}}
Вектор tundefined\overrightarrow{\mathrm{t}} представлен суммой векторов mundefinednnundefined\overrightarrow{\mathrm{m}}{ }_{n} \overrightarrow{\mathrm{n}}

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Problem 116

Suppose that v=22\|\vec{v}\|=22 and w=6\|\vec{w}\|=6. Suppose also that, when drawn starting at the same point, v\vec{v} and w\vec{w} make an angle of 5π6\frac{5 \pi}{6} radians. (A.) Find w+v\|\vec{w}+\vec{v}\| and round to two decimal places. w+v=\|\vec{w}+\vec{v}\|=\square (B.) Find wv\|\vec{w}-\vec{v}\| and round to two decimal places. wv=\|\vec{w}-\vec{v}\|=

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Problem 117

Übung 19 Bestimmen Sie den Schnittpunkt und den Schnittwinkel der Geraden g und h . a) g:xundefined=(12)+r(31), h:xundefined=(41)+s(11)\mathrm{g}: \overrightarrow{\mathrm{x}}=\binom{1}{2}+\mathrm{r}\binom{3}{1}, \mathrm{~h}: \overrightarrow{\mathrm{x}}=\binom{4}{1}+\mathrm{s}\binom{1}{1} b) g:x=(314)+r(222),h:x=(231)+s(123)g: \vec{x}=\left(\begin{array}{l}3 \\ 1 \\ 4\end{array}\right)+r\left(\begin{array}{r}2 \\ 2 \\ -2\end{array}\right), h: \vec{x}=\left(\begin{array}{r}2 \\ 3 \\ -1\end{array}\right)+s\left(\begin{array}{r}1 \\ 2 \\ -3\end{array}\right) c) gg durch A(21)A(2 \mid 1) und B(32)B(3 \mid 2), d) gg durch A(325)A(3|2| 5) und B(563)B(5|6| 3), hh durch C(27)C(2 \mid 7) und D(45)D(4 \mid 5) hh durch C(437)C(4|3| 7) und D(264)D(-2|-6| 4)

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Problem 118

A pulse of radiation propagates with velocity vector v=<0,0,c\vec{v}=<0,0,-c\rangle. The electric field in the pulse is E=4×106,0,0>N/C\vec{E}=\left\langle 4 \times 10^{6}, 0,0>N / C\right.. What is the magnetic field in the pulse? B=<0\vec{B}=<0 \square 75-75 , \square 0 >T>T

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Problem 119

The point W(5,2)W(5,-2) is reflected over the yy-axis. What are the coordinates of the resulting point, W'? W(W^{\prime}( \square , \square

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Problem 120

From AA to BB a private plane flies 1.5 hours at 110 mph on a bearing of 2929^{\circ}. It turns at point BB and continues another 2.2 hours at the same speed, but on a bearing of 119119^{\circ} to point CC. Round each answer to three decimal places.
At the end of this time, how far is the plane from its starting point? \square miles
On what bearing is the plane from its original location? \square degrees

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Problem 121

Questions 14 and 15 refer to the following.
Four forces of equal magnitude are exerted on a square at the locations and in the directions indicated in the figure. Points A and B are labeled for reference. 15 Mark for Review
Which of the forces, if any, exerts zero torque about Point B? (A) F1F_{1} (B) F3F_{3} (C) Both F1F_{1} and F3F_{3} (D) None of the forces exert zero torque about Point B

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Problem 122

Four points A, B, C, D on a semicircle satisfy ABundefined=BCundefined=CDundefined|\overrightarrow{\mathrm{AB}}|=|\overrightarrow{\mathrm{BC}}|=|\overrightarrow{\mathrm{CD}}|. Assess the validity of assertions A and R.

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Problem 123

¿Cuáles son magnitudes vectoriales? a. desplazamiento, trabajo, energía b. fuerza, aceleración, temperatura c. aceleración, masa, tiempo d. velocidad, desplazamiento, fuerza

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Problem 124

Un vector tiene magnitud y dirección, mientras que un escalar solo tiene magnitud. ¿Cuál es la diferencia?

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Problem 125

Calcula la magnitud de un vector con x=3x=3 y y=2y=2. Opciones: a. 5 b. 3.6 c. 6 d. 1

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Problem 126

La magnitud de un vector unitario es igual a: a. mayor a uno. b. suma de componentes al cuadrado\sqrt{\text{suma de componentes al cuadrado}}. c. múltiplo de la magnitud del vector desplazamiento. d. igual a 1.

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Problem 127

Three charges of +6.65μC+6.65 \mu \mathrm{C} at the triangle's vertices create a force. Find the resultant force: a. 172.34 N172.34 \mathrm{~N} b. 22.98 N22.98 \mathrm{~N} c. 34.47 N34.47 \mathrm{~N} d. 68.94 N68.94 \mathrm{~N} e. 0.89 N0.89 \mathrm{~N}

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Problem 128

Determine the location of the point (3,4)(-3,4) in the coordinate plane.

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Problem 129

Evaluate Fdr\int F \cdot dr for fˉ=xyiˉzj^+x2kˉ\bar{f}=x y \bar{i}-z \hat{j}+x^{2} \bar{k} along α:x=t2,y=2t,z=t3\alpha: x=t^{2}, y=2t, z=t^{3} from t=0t=0 to t=1t=1. Ans: 5170\frac{51}{70}

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Problem 130

Evaluate Fdr\int F \cdot d r for Fˉ=xyiˉzj+x2kˉ\bar{F}=x y \bar{i}-z j+x^{2} \bar{k} along the curve x=t2,y=2t,z=t3x=t^{2}, y=2t, z=t^{3} from t=0t=0 to t=1t=1.

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Problem 131

Evaluate Fdr\int F \cdot d r for Fˉ=xyiˉzj+x2kˉ\bar{F}=x y \bar{i}-z j+x^{2} \bar{k} along the curve x=t2x=t^{2}, y=2ty=2t, z=t3z=t^{3} from t=0t=0 to t=1t=1. Answer: 5170\frac{51}{70}.

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Problem 132

Calculate the work done by the force fˉ=zˉiˉ+xjˉ+yk^\bar{f}=\bar{z} \bar{i}+x \bar{j}+y \hat{k} along the curve rˉ=costi+sintjtkˉ\bar{r}=\cos t i+\sin t j-t \bar{k} from t=0t=0 to t=2πt=2 \pi.

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Problem 133

Evaluate C(yzdl+xzdy+lydz)\oint_{C}(y z \, dl + x z \, dy + l y \, dz) for the helix x=acost,y=asint,z=ktx=a \cos t, y=a \sin t, z=k t as tt goes from 0 to 2π2\pi.

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Problem 134

Translate Triangle RST with vertices R(4,2)R (-4,2), S(5,3)S (5,3), T(2,5)T (2,-5), 4 down and 3 left. Find new coordinates.

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Problem 135

xencises 16.9.
1. Using F=3x,y3,2z2\mathbf{F}=\left\langle 3 x, y^{3},-2 z^{2}\right\rangle and the region bounded by x2+y2=9,z=0x^{2}+y^{2}=9, z=0, and z=5z=5, compute both integrals from the Divergence Theorem. \Rightarrow

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Problem 136

2. Let EE be the volume described by 0xa,0yb,0zc0 \leq x \leq a, 0 \leq y \leq b, 0 \leq z \leq c, and F=x2,y2,z2\mathbf{F}=\left\langle x^{2}, y^{2}, z^{2}\right\rangle. Compute FNdS\iint \mathbf{F} \cdot \mathbf{N} d S \Rightarrow

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Problem 137

4. Let EE be the volume described by 0x1,0yx,0zx+y0 \leq x \leq 1,0 \leq y \leq x, 0 \leq z \leq x+y, and F=x,2y,3z\mathbf{F}=\langle x, 2 y, 3 z\rangle. Compute EFNdS.\iint_{\partial E} \mathbf{F} \cdot \mathbf{N} d S . \Rightarrow

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Problem 138

11. Given the following two vectors in the 7th 7^{\text {th }} dimensions. Find their scalar product (i.e. AB\vec{A} \cdot \vec{B} ): A=(0165320),B=(1240534)\vec{A}=\left(\begin{array}{c} 0 \\ 1 \\ -6 \\ 5 \\ 3 \\ 2 \\ 0 \end{array}\right), \vec{B}=\left(\begin{array}{c} 1 \\ 2 \\ 4 \\ 0 \\ 5 \\ -3 \\ 4 \end{array}\right) a. 1 b. 24 c. -3 d. -13 e. -17

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Problem 139

Three long wires are parallel to the zz axis, and each carries a current of 10 A in the positive zz direction. Their points of intersection with the xyx y plane form an equilateral triangle with sides of 50 cm , as shown in the figure. A fourth wire (wire b) passes through the midpoint of the base of the triangle and is parallel to the other three wires. If the net magnetic force on wire aa is zero, what are the (a) size and (b) direction ( +z+z or z-z ) of the current in wire bb ?

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Problem 140

7. In the graph, the translation vector maps ABC\triangle A B C to ABC\triangle A^{\prime} B^{\prime} C^{\prime}.

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Problem 141

5. Find the vector and parametric equation of the line that passes through the point (2,1,0)(2,1,0) and parallel to v=<2,1,5>v=<2,-1,5>.

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Problem 142

2. What is the magnitude of resultant vector where u=42,2 and v=52,3\vec{u}=\langle-4 \sqrt{2},-2\rangle \text { and } \vec{v}=\langle 5 \sqrt{2}, 3\rangle

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Problem 143

Check if the following vectors are linearly independent in R3:\text{Check if the following vectors are linearly independent in } \mathbb{R}^3: (i)[102],[013], and [115](\mathrm{i}) \quad \begin{bmatrix} 1 \\ 0 \\ 2 \end{bmatrix}, \begin{bmatrix} 0 \\ 1 \\ 3 \end{bmatrix}, \text{ and } \begin{bmatrix} -1 \\ -1 \\ -5 \end{bmatrix} (j)[111],[210],[301], and [222](\mathrm{j}) \quad \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}, \begin{bmatrix} 2 \\ 1 \\ 0 \end{bmatrix}, \begin{bmatrix} 3 \\ 0 \\ 1 \end{bmatrix}, \text{ and } \begin{bmatrix} 2 \\ 2 \\ 2 \end{bmatrix}

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Problem 144

Find point BB on line segment ACAC where A(6,6)A(6,-6), C(6,2)C(-6,-2), and AB=34ACAB=\frac{3}{4}AC.

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Problem 145

Gegeben sind die Punkte A(2,-3,0), B(2,2,0), C(-1,2,0) und E(2,-3,5) eines Quaders. Finde die anderen Eckpunkte und berechne die Diagonale AG\overline{A G}.

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Problem 146

Berechnen Sie die Vektor-Koordinaten aus den folgenden Linearkombinationen: a) (213)+(145)+2(114)\left(\begin{array}{l}2 \\ 1 \\ 3\end{array}\right)+\left(\begin{array}{r}1 \\ 4 \\ -5\end{array}\right)+2 \cdot\left(\begin{array}{l}1 \\ 1 \\ 4\end{array}\right) b) 3(2100)+2(031)5(111)3 \cdot\left(\begin{array}{r}2 \\ 10 \\ 0\end{array}\right)+2 \cdot\left(\begin{array}{r}0 \\ 3 \\ -1\end{array}\right)-5 \cdot\left(\begin{array}{l}1 \\ 1 \\ 1\end{array}\right) c) 12(312)+13(122)14(224)\frac{1}{2} \cdot\left(\begin{array}{l}3 \\ 1 \\ 2\end{array}\right)+\frac{1}{3} \cdot\left(\begin{array}{r}1 \\ 2 \\ -2\end{array}\right)-\frac{1}{4} \cdot\left(\begin{array}{l}2 \\ 2 \\ 4\end{array}\right)

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Problem 147

Gegeben sind die Punkte A(2|-3|0), B(2|2|0), C(-1|2|0) und E(2|-3|5) eines Quaders. Finde die anderen Eckpunkte und die Länge der Diagonale AG\overline{A G}.

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Problem 148

Find the projection of the vector u=3i+j+ku=3 i+j+k onto the vector a=4j3ka=4 j-3 k.

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Problem 149

Find the component of the vector a=3i+jka=3i+j-k in the direction of b=i2j+6kb=i-2j+6k.

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Problem 150

Find the new vertices K,L,M,NK^{\prime}, L^{\prime}, M^{\prime}, N^{\prime} after rotating polygon KLMN by 9090^{\circ} clockwise.

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Problem 151

Given lines OAN,OMBO A N, O M B and APBA P B, with AN=2OAA N = 2 O A. If MM is the midpoint of OBO B, find kk in APundefined=kABundefined\overrightarrow{A P} = k \overrightarrow{A B}, given MPNMPN is straight.

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Problem 152

In which direction in this diagram is there a net force of 200 N? right up down left 1 2 3

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Problem 153

In this diagram, an object is represented by the circle and the arrows represent the forces acting on the object. How would the object be expected to behave if it starts out not moving? speed up moving to the right move to the left at a constant speed move to the right at a constant speed speed up moving to the left

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Problem 154

Evaluate the line integral CFdr\int_{C} \mathbf{F} \cdot d \mathbf{r}, where CC is given by the vector function r(t)\mathbf{r}(t). F(x,y,z)=sin(x)i+cos(y)j+xzkr(t)=t5it3j+tk,0t1\begin{array}{l} \mathbf{F}(x, y, z)=\sin (x) \mathbf{i}+\cos (y) \mathbf{j}+x z \mathbf{k} \\ \mathbf{r}(t)=t^{5} \mathbf{i}-t^{3} \mathbf{j}+t \mathbf{k}, 0 \leq t \leq 1 \end{array}

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Problem 155

4. Al punto B en este plano cartesiano, se le aplica una homotecia de centro AA y factor 2. ¿Cuáles son las coordenadas del punto que se obtiene?
A (4;3)(4 ; 3) (B) (10;6)(10 ; 6) (C) (12;8)(12 ; 8) (D) (14;8)(14 ; 8)

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Problem 156

AA and BB shown below, find 16A+B-\frac{1}{6} A+B A=[2436]B=[82]A=\left[\begin{array}{l} -24 \\ -36 \end{array}\right] \quad B=\left[\begin{array}{l} -8 \\ -2 \end{array}\right]

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Problem 157

Dilate FGH\triangle F G H by a scale factor of 4 with the center of dilation at the origin.
How can you use the coordinates of point FF to find the coordinates of point FF^{\prime} ?
Add 4 to each coordinate.
Subtract 4 from each coordinate.
Multiply each coordinate by 4.
Divide each coordinate by 4.

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Problem 158

40. Let F(x,y,z)=3x2yi+(x3+y3)j\mathbf{F}(x, y, z)=3 x^{2} y \mathbf{i}+\left(x^{3}+y^{3}\right) \mathbf{j}. (a) Verify that curl F=0\mathbf{F}=\mathbf{0}. (b) Find a function ff such that F=f\mathbf{F}=\nabla f. (Techniques for constructing ff in general are given in Chapter The one in this problem should be sought by trial and error. 1

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Problem 159

L'accélération est un vecteur dirigé dans le sens du mouvement. (Acceleration is a vecior directed in the direction of motion).
Select one: Vrai (True) Faux. (False)

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Problem 160

,nsider parallelogram JKLMJ K L M below.
Note that JKLMJ K L M has vertices J(6,2),K(1,6),L(7,1)J(-6,-2), K(-1,6), L(7,1), and Answer the following to determine if the parallelogram is a rectangle, (a) Find the length of JK\overline{J K} and the length of a side adjacent to JK\overline{J K}. Give exact answers (not decimal approximations).
Length of JK\overline{J K} : \square
Length of side adjacent to JK\overline{J K} : \square

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Problem 161

Use the figure to evaluate a+b,ab\mathbf{a}+\mathbf{b}, \mathbf{a}-\mathbf{b}, and a-\mathbf{a}. a+b=[a+b=\langle[ \square \square 77\rangle

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Problem 162

Describe the symbols: alou PQundefined\overleftrightarrow{P Q}, PQundefined\overrightarrow{P Q}, PQundefined\overrightarrow{P Q}, QPundefined\overrightarrow{Q P}.

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Problem 163

Find the midpoint MM of the line segment with endpoints G(5,4)G(5,4) and H(7,4)H(7,4). Write MM as decimals or integers. M=M=

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Problem 164

Rotate the vector (5,3)(-5,3) using the matrix [0110]\left[\begin{array}{cc}0 & 1 \\ -1 & 0\end{array}\right]. Find the terminal xx-value. x= x=

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Problem 165

Rotate the vector [53]\begin{bmatrix}-5 \\ -3\end{bmatrix} using the matrix [0110]\begin{bmatrix}0 & 1 \\ -1 & 0\end{bmatrix}. Find the xx-value of the new vector. x= x=

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Problem 166

John cycles south 15 m, east 21 m, then south 5 m to point Y. Calculate the distance from X to Y.

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Problem 167

Find the distance and bearing from Corpus Christi to the Coast Guard cutter after it travels at 30 knots for 4 hours on given courses.

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Problem 168

A boat travels at 40 knots on a course of 6565^{\circ} for 2 hours, then 155155^{\circ} for 4 hours. Find the distance and bearing from Fort Lauderdale.

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Problem 169

Find the vertices of parallelogram ABCDA^{\prime \prime} B^{\prime \prime} C^{\prime \prime} D^{\prime \prime} after dilation by 4 and reflection. Are the parallelograms similar or congruent?

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Problem 170

Find the midpoint of the segment with endpoints (5,11)(5,11) and (3,1)(3,1).

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Problem 171

Find the midpoint of the line segment between the points (2,4)(-2,4) and (2,6)(2,6).

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Problem 172

Find the midpoint of the segment between the points (7,5)(-7,5) and (7,7)(7,7).

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Problem 173

Q6 consider the vectors (5) x(1)(t)=[t1],x(2)=[t22t]x^{(1)}(t)=\left[\begin{array}{l} t \\ 1 \end{array}\right], x^{(2)}=\left[\begin{array}{c} t^{2} \\ 2 t \end{array}\right] (1) find w(x(1),x(2))w\left(x^{(1)}, x^{(2)}\right) (2) In what intervals are x(1),x(2)x^{(1)}, x^{(2)} linealy inelep? (3) what eonatitions conclutions can be drawn about the coefficients in the systeme of homogenons DE's statisfied by x(1)x(2)x^{(1)} x^{(2)}

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Problem 174

```latex \text{صورة النقطة } (3, -2) \text{ بالانسحاب 4 وحدات لليسار و 3 وحدات للأعلى هي النقطة:} ```

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Problem 175

40- Two vectors have magnitudes of 10 m and 15 m . The angle between them when they are drawn with their tails at the same point is 6565^{\circ}. The component of the longer vector along the line of the shorter is: A. 0 B. 4.2 m C. 6.3 m D. 9.1 m E. 14 m

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Problem 176

Use the flux form of Green's Theorem to find the outward flux of F=10x,19y\mathbf{F}=\langle 10 x, 19 y\rangle across the boundary of the circle x2+y2=1x^{2}+y^{2}=1.
Flux = \square

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Problem 177

9. Triangle ABCA B C is dilated about the origin with a scale factor of 3 to make Triangle ABCA^{\prime} B^{\prime} C^{\prime}. Determine the coordinates of AA^{\prime}. A) (3,12)(3,12) B) (1,0)(-1,0) C) (12,3)(-12,3) D) (6,9)(-6,9)

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Problem 178

9. Triangle ABCA B C is dilated about the origin with a scale factor of 3 to make Triangle ABCA^{\prime} B^{\prime} C^{\prime}. Determine the coordinates of AA^{\prime}. A) (3,12)(3,12) B) (1,0)(-1,0) C) (12,3)(-12,3) D) (6,9)(-6,9)

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Problem 179

(1.24) Show that A,B\boldsymbol{A}, \boldsymbol{B}, and C\boldsymbol{C} are linearly dependent if AB×C=0\boldsymbol{A} \cdot \boldsymbol{B} \times \boldsymbol{C}=0.

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Problem 180

Sketch an angle θ\theta with the point (6,0)(-6,0) on its terminal side. Find the six trig functions of θ\theta.

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Problem 181

A proton is fired with a speed of 0.90×106 m/s0.90 \times 10^{6} \mathrm{~m} / \mathrm{s} through the parallel-plate capacitor shown in (Figure 1). The capacitor's electric field is E=(0.50×105 V/m, down )\vec{E}=\left(0.50 \times 10^{5} \mathrm{~V} / \mathrm{m}, \text { down }\right)
Part A
What is the strength of the magnetic field B\vec{B} that must be applied to allow the proton to pass through the capacitor with no change in speed or direction? Express your answer with the appropriate units.

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Problem 182

8) [swHW part(b), seHW part(a)] Consider two linearly-polarized plane wave pulses of light with the same duration, the same wavelength, the same polarization, and the same maximum amplitude, and propagating in vacuum in exactly-opposite directions. The pair will form a standing electric field wave in places where they overlap. As we know, such a standing wave momentarily has zero electric field amplitude everywhere at one infinitesimal instant in time, and thus the two combined waves must, at some single instant in time, have zero electric field everywhere in space.
PHY-2112 Duplication or distribution prohibited without express written consent from Stephen Fahey. a) At the one instant in time when the two pulses result in zero electric field everywhere in space, describe the magnetic field everywhere in space. b) Propose an explanation of how the energy of a standing light wave is stored when the electric field is zero everywhere in space. For your answer please propose a testable hypothesis that is consistent with all the laws of physics that you know. Be sure your hypothesis could potentially be disproven (this is called a "falsifiable" hypothesis, and is considered a stronger type of scientific hypothesis).

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Problem 183

1. [\#241] Sailing - wind speed 1 poin
A sailor sailing due north at 5 knots observes an apparent wind moving at 5 knots directly from the boat's starboard (right hand) side, i.e. at 9090^{\circ} to the axis of the boat. What is the 'true' wind speed? (i.e. what is the speed of the wind with respect to the ground?).
The 'true' wind speed is \qquad knots.
Enter answer here

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Problem 184

(1 point)
Let WW be the set of all vectors of the form [2s+3t5s+2t4st]\left[\begin{array}{c}2 s+3 t \\ 5 s+2 t \\ 4 s-t\end{array}\right]. Find vectors w~\tilde{w} and zz in R3\mathbb{R}^{3} such that W=span{z~undefined,}\mathbb{W}=\operatorname{span}\{\overrightarrow{\tilde{z}}, \vec{\nabla}\}. u=[]v=[]\vec{u}=\left[\begin{array}{l} \square \\ \square \\ \square \end{array}\right] \cdot \vec{v}=\left[\begin{array}{c} \square \\ \square \\ \square \end{array}\right]

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Problem 185

Give a vector parametric equation for the line through the point (4,5,5)(4,5,5) that is parallel to the line 2,44t,5+5t\langle-2,-4-4 t, 5+5 t\rangle : L(t)=L(t)= \square Preview Mv Answers Submit Answere

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Problem 186

Suppose a line is given parametrically by the equation L(t)=14t,43t,4tL(t)=\langle 1-4 t, 4-3 t, 4-t\rangle
Then the vector and point that were used to define this line were vˉ=\bar{v}= \square , and p=p= \square (1,4,4)(1,4,4)

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Problem 187

Points P,Q,RP, Q, R and SS have position vectors p=(63),q=(35),r=(13)\mathbf{p}=\binom{6}{3}, \mathbf{q}=\binom{-3}{-5}, \mathbf{r}=\binom{1}{-3} and s=(105)\mathbf{s}=\binom{10}{5} Prove that the quadrilateral PQRSP Q R S is a parallelogram.

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Problem 188

A million years ago, an alien species built a vertical tower on a horizontal plane. When they returned they discovered that the ground had tilted so that measurements of 3 points on the ground gave coordinates of (0,0,0),(1,1,0)(0,0,0),(1,1,0), and (0,2,3)(0,2,3). By what angle does the tower now deviate from the vertical? \square radians.

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Problem 189

Find the new coordinates of B (-5,-8), C (-5,-3), D (0,-3), E (0,-8) after a 180180^{\circ} rotation around the origin.

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Problem 190

Find the new coordinates of vertices B (2,9)(2,-9), C (2,4)(2,-4), and D (1,9)(1,-9) after a 270270^{\circ} clockwise rotation.

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Problem 191

A train starts from rest. After 40 s, it reaches 60 m/s. What is its acceleration?

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Problem 192

Find the length of the altitude in ABC\triangle \mathrm{ABC} from B Given: A(0,2),B(3,7),C(5,3)\mathrm{A}(0,2), \mathrm{B}(3,7), \mathrm{C}(5,3) Extra Credit: Find the parametric vector equation and standard

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Problem 193

4. Convert the rectangular coordinates to polar coordinates with r>0r>0 and 0θ<2π0 \leq \theta<2 \pi. a. (1,1)(-1,1) b. (33,3)(3 \sqrt{3},-3)

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Problem 194

Your colleague is trying to create a vector of vectors to store a matrix of characters. Here's the program they have written to practice with this vector of vectors: ``` #include #include using namespace std; int main() { vector row(3,'*'); vector < vector > matrix(4,row); // chanġe some elements matrix.at(0).at(2) = '8'; matrix.at(1).at(0) = 'G'; matrix.at(3),at(1) = '%'; matrix.at(1).at(2) = '.'; matrix.at(0).at(1) = '@'; matrix.at(2).at(0) = 'B'; /// print the matrix for (size_t i = 0; i < matrix.size(); ++i) { for (size_t j = 0; j < matrix.size(); ++j) { } cout << matrix.at(i).at(j); } cout << endl; } ```
This code is supposed to print this to the terminal: *@8 G*. B** *8*
But the program doesn't work! What is the best description of the bug in this program? The vector of vectors wasn't initialized correctly. The inner loop needs to iterate until the size of the inner vector is reached; right now, it's iterating based on the size of the outer vector. The order of the indexing is wrong in the cout statement that prints the element. The outer loop needs to iterate until the size of the outer vector is reached; right now, it's iterating based on the size of the inner vector.

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Problem 195

Decompose v\mathbf{v} into two vectors v1\mathbf{v}_{1} and v2\mathbf{v}_{2}, where v1\mathbf{v}_{1} is parallel to w\mathbf{w} and v2\mathbf{v}_{2} is orthogonal to w\mathbf{w}. v=8i2j and w=i+jv=-8 i-2 j \text { and } w=-i+j
What does v1v_{1} equal? 3i+3j-3 i+3 j 5i+5j3i3j\begin{array}{l} 5 i+5 j \\ 3 i-3 j \end{array} 5i5j-5 i-5 j What does v2\mathrm{v}_{2} equal? 3i3j3 i-3 j 3i+3j-3 i+3 j 5i+5j5 i+5 j 5i5j-5 i-5 j

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Problem 196

1. In the diagram below, a force, FF, is applied to the handle of a lawnmower inclined at angle θ\theta to the ground.
The magnitude of the horizontal component of force FF depends on A) the magnitude of force FF, only B) the measure of angle θ\theta, only C) both the magnitude of force FF and the measure of angle 0 D) neither the magnitude of force FF nor the measure of angle θ\theta \therefore Base your answer to the following question on the information and diagram below. A child kicks a ball with an initial velocity of 8.5 meters per second at an angle of 3535^{\circ} with the horizontal, as shown. The ball has an initial vertical velocity of 4.9 meters per second and a total time of flight of 1.0 second. [Neglect air resistance.]
The horizontal component of the ball's initial velocity is approximately A) 3.6 m/s3.6 \mathrm{~m} / \mathrm{s} B) 7.0 m/s7.0 \mathrm{~m} / \mathrm{s} C) 4.9 m/s4.9 \mathrm{~m} / \mathrm{s} D) 13 m/s13 \mathrm{~m} / \mathrm{s} i. Base your answer to the following question on the diagram below which represents a ball being kicked by a foot and rising at an angle of 30.30 .^{\circ} from the horizontal. The ball has an initial velocity of 5.0 meters per second. [Neglect friction.]
As the ball rises, the vertical component of its velocity A) decreases B) increases C) remains the same
4. As the angle between a force and level ground decreases from 616^{1} to 3030^{\circ}, the vertical component of the force A) decreases B) increases C) remains the same
5. A force of 100 . Newtons is applied to an object at an angle of 3C3 C from the horizontal as shown in the diagram below. What is the magnitude of the vertical component of this force? A) 0 N B) 50.0 N C) 86.7 N D) 100.N100 . \mathrm{N}
6. The diagram below shows a child pulling a 50 .-kilogram friend on a sled by applying a 300 --newton force on the sled rope at an angle of 4040^{\circ} with the horizontal.

The vertical component of the 300 .-newton force is approximately A) 510 N B) 230 N C) 190 N D) 32 N
7. The vector diagram below represents the horizontal component, H , and the vertical component, FF, of a 24 -newton force acting at 3535^{\circ} above the horizontal.

What are the magnitudes of the horizontal and vertical components? A) FH=3.5 NF_{H}=3.5 \mathrm{~N} and FV=4.9 NF_{V}=4.9 \mathrm{~N} B) FH=4.9 NF_{H}=4.9 \mathrm{~N} and FV=3.5 NF_{V}=3.5 \mathrm{~N} C) FH=14 NF_{H}=14 \mathrm{~N} and FV=20.NF_{V}=20 . \mathrm{N} D) FH=20.NF_{H}=20 . \mathrm{N} and FV=14 NF_{V}=14 \mathrm{~N} Page I

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Problem 197

Given u=1+2j+k,v=3i+j+2k\quad u=1+2 j+k, v=3 i+j+2 k, find the following cross products:

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Problem 198

Iname: Jude Elsayed Date: 2024-11-25
Official Time: 11:38:00
Question 3 [10 points] Give a basis for span(S), where SS is the set given below. {[001],[212],[1059],[639]}\left\{\left[\begin{array}{l} 0 \\ 0 \\ 1 \end{array}\right],\left[\begin{array}{c} -2 \\ 1 \\ 2 \end{array}\right],\left[\begin{array}{c} 10 \\ -5 \\ -9 \end{array}\right],\left[\begin{array}{c} 6 \\ -3 \\ -9 \end{array}\right]\right\}
Number of Vectors: 1 {[0002}\left\{\left[\begin{array}{l} 0 \\ 0 \\ 0_{2} \end{array}\right\}\right.

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Problem 199

orem, 17.8 .29 Points: 0 of 1 Save
Use the Divergence Theorem to compute the net outward flux of the vector field F=x2,y2,z2F=\left\langle x^{2},-y^{2}, z^{2}\right\rangle across the boundary of the region DD, where DD is the region in the first octant between the planes z=6xyz=6-x-y and z=3xyz=3-x-y.
The net outward flux is \square . (Type an exact answer, using π\pi as needed.)

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Problem 200

After 4 seconds, where is the sprite located? Choose from: (25,-25), (-25,0), (0,25), (-25,25).

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