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.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.