Graph the image of square TUVW after a rotation 90° counterclockwise around the origin.104-10 -8 -6Submit-4 -28642-2-46-810246OPWT8VU10Work it outVideo C

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Answered: Graph the image of square TUVW after a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A square ABCD graphed on the coordinate plane with endpoints A(3, 2) and C(1, -2). Determine the coordinates of the other diagonal.
Graph the image of square TUVW after a rotation 90° counterclockwise around the origin. 104 8- 9 -6- -4- 2- -10 -8 -6 -4 -2 2 4 6 8 00 --2- -4- W V -6- T U -8- -10 10 X
Let the transformation T : IR³ →R² be given by the formula T(x,,X2,X3) = (2x, –x,, X, +3x;). Find the standard matrix of this transformation and write it in matrix multiplication form. Check correctness of your answer for the point (1,4,-3).
(part 1 of 4) Suppose you start at the origin in 3-space, move along the x-axis a distance of 2 units in the positive direction, and then move down- ward a distance of 3 units. What are the coordinates of your position? 1. (2,0, -3) 2. (2, -3,0) 3. (2,0,3) 4. (0, 2, -3) 5. (0, -3,2) (part 2 of 4) Which one of the points P(6, 9, -3), Q(8, -2, -8), R(-5, 8, 1) in 3-space is closest to the xz-plane? 1. R(-5, 8, 1) 2. P(6, 9, -3) 3. Q(8, -2, -8) (part 3 of 4) A rectangular box is constructed in 3-space with one corner at the origin and other ver- tices at (1,0,0), (0,3,0), (0,0,2). Find the length of the diagonal of the box. 1. length 14 2. length 3. length 4. length 5. length 6. length = = = = √22 √14 √19 19 22 (part 4 of 4) What are the coordinates of the projection of the point Q(-4, 5, 3) onto the zx-plane? 1. (-4, 0, 3) 2. (-4, -5, 3) (4, 5, 3) 3. 4. (-4, 5, 0) 5. (-4, 5, -3) 6. (0,5, 3)
Find an equation the plane that passes through the points A(4,0, –5), B(8,-3,-6), and C (1, 2, -1). Write your final answer in standard form.
What is the center of the shape formed by the equation (y+5)² = 1? 25 O (0,0) O (-3,5) O (3,-5) O (9,25) (-9, -25) (x-3)² 49
2. Use grid paper. Draw and label a coordinate grid. Plot each ordered pair. Explain how you moved to do this. F(3, 5) G(6, 7) H(9, 2) 1(1, 10) J(7, 0) 3. a) Point A has coordinates (0, 17). What do you know about Point A? b) Point B has coordinates (24, 0). What do you know about Point B? c) What is the location of a point with coordinates (0, 0)? How do you know?

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Graph the image of square TUVW after a rotation 90° counterclockwise around the origin. -10 -8 -6 Submit -2 8 6 4 2 -2 6 -8 -10 2 4 6 W T 8 V U 10 Work it out