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U 2 A) 4 d vector space V such that -001 - 402. Find the change-of-coordinates matrix from B to C. B) D) 1 67 1-3-4 For the given matrix and eigenvalue, find an eigenvector corresponding to the eigenvalue. A = -20 612_2 15.09 |-72 22 A) B) 17 C)
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Groupwork: Kinematics and Forces Review If vector A = (4,5) and vector B-6,-7), calculate: 1.1 A+B 1.2 A-B 1.3 A-B 1.4 Convert both A and B into polar coordinates and draw them on a graph 2 A particle starts at the origin, Its initial velocity is 4m's in the x direction. Its acceleration is given by a-3sin(20). What are the values of a, v and As after 10s? Page 1 Feb. 28, 2018
Find the resultant vector in both polar and rectangular coordinates. Likewise, sketch it. Refer to the vectors . A (2 cm,45) . B (2 cm, 90) e C (2 cm, 180) . D (2 cm, 270) . E (2 cm, 60) . F (2 cm,0) R 2D + A -8 6 4 2 Polar Coordinates: Rectangular Coordinates R 2(E F) 64 -2 Polar Coordinates: Rectangular Coordinates: Extra Credit R 3(A -2(D+B) +F) + 2C-3B -8 -6 42 -6 Polar Coordinates:...
4. Given a point (-3,-) in polar representation, answer each question. a) Plot the point b) Find two additional polar representations, using -2n< < 26 c) Convert to rectangular coordinates. 5. Convert the rectangular point (V3.1) to polar coordinates where 0 <<2 6. Given a polar equation r = 4sin e a) Sketch the graph of the polar equation by completing the table. r 0 FT/6 1/2 5/6 b) Convert the polar equation into a rectangular equation,
16) Find the magnitude and the direction of the vector w = <583-52 02150 d) =20, 0-240° b) 131=20, G = 150° e) W310, 0-330° (c) 1 2 1 2 10 0=240 92)=20, 0-330 (a) 11:10,
(b) You are given the point (2, -1/6) in polar coordinates. (0) Find another pair of polar coordinates for this point such that r >0 and 21 < a < 41. r= 2 0 = 23pi/6 (ii) Find another pair of polar coordinates for this point such that r <0 and 0 <o< 27. = -2 0 = 5pi/6 (c) You are given the point (-2, -1/4) in polar coordinates. () Find another pair of polar coordinates for this point...
Let A = {21,22,23) and B = {b,b2,63} be bases for a vector space V, and suppose a, = 5b, - b», a = -b + b + b3, az = b2 - 253 a Find the change-of-coordinates matrix from A to B. b. Find [x]g for x = 3a + 4a, +az. а PE BA b. [xlg (Simplify your answers.)
Find the resultant vector in both polar and rectangular coordinates. Likewise, sketch it. Refer to the vectors 2 cm, 45° cm,90 . C (2 cm, 180°) . D (2 cm, 270°) . E (2 cm, 60°) . E (2 cm, 0) R-2(E-F) -8 64 -2 -4 Polar Coordinates: Rectangular Coordinates: R=2D + A -8 -64 2 -8 Polar Coordinates: Rectangular Coordinates:
In the vector space R, let 8 {(1,3,0), (1, -3, 0), (0, 2, 2)}. (a) (6 points) Show that y is a basis of R3. (b) (7 points) Find the matrix [I,where I is the identity transform R3 R3 (c) (7 points) Using the matrix [I, convert the vector (r, y, z) into coordinates with respect to y instead of B. In other words, find ((x, y, z)] {(1,0,0), (0, 1,0), (0,0, 1)} be the standard basis, and let
1. The Cartesian coordinates representation of a vector is (65 cm/s, 32 cm/s), the polar coordinates of this vector are: Select one: a. (72 cm/s, 26 degrees) b. (52 cm/s, 63 degrees) c. (45 cm/s, 15 degrees) d. (26 cm/s, 72 degrees) 2. Which of the following correctly expresses the vector 29 m at 29 degrees in unit vector notation Select one: a. (15 i + 43 j) m b. (25 i + 14 j) m c. (14 i +...