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Let 0 € [0, 27). Let A = cos 0 - sin sin 0 cos 0 ve R². (1) What is the length of Av, in terms of |v|? (2) What is the angle between Av and v, in terms of 0? (3) In the following picture, the red ellipse is defined by x² + ry+y? = 1, and the blue 22 3y? + 2 ellipse is defined by 1. -2 2 Find a 2 x 2 matrix B such that applying B to the red ellipse results in the blue ellipse.

Let 0 € [0, 27). Let A = cos 0 - sin sin 0 cos 0 ve R². (1) What is the length of Av, in terms of |v|? (2) What is the angle between Av and v, in terms of 0? (3) In the following picture, the red ellipse is defined by x² + ry+y? = 1, and the blue 22 3y? + 2 ellipse is defined by 1. -2 2 Find a 2 x 2 matrix B such that applying B to the red ellipse results in the blue ellipse.

Advanced Engineering Mathematics
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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Let 0 € [0, 27). Let A = cos 0 - sin sin 0 cos e ve R². (1) What is the length of Av, in terms of |v|? (2) What is the angle between Av and v, in terms of 0? (3) In the following picture, the red ellipse is defined by ² + xy+y? = 1, and the blue 22 3y? ellipse is defined by + = 1. 2 -2 2 Find a 2 x 2 matrix B such that applying B to the red ellipse results in the blue ellipse.
Transcribed Image Text:Let 0 € [0, 27). Let A = cos 0 - sin sin 0 cos e ve R². (1) What is the length of Av, in terms of |v|? (2) What is the angle between Av and v, in terms of 0? (3) In the following picture, the red ellipse is defined by ² + xy+y? = 1, and the blue 22 3y? ellipse is defined by + = 1. 2 -2 2 Find a 2 x 2 matrix B such that applying B to the red ellipse results in the blue ellipse.
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