a) Prove that B(x, y) (x, y) for all (x, y) R2 b) Let (x, y) R2 be a nonzero vector and represent the angle between B(x, y) and (x, y) Prove that cos cos Thus, show that B rotates R2 through an angle (When 0, we shall call B counterclockwise rotation about the origin through the angle 0 ) Let for s...

By definition Bx y x cos y sin x si ...

a) Prove that ||B(x, y)|| = ||(x, y)|| for all (x, y) R2. b) Let (x,

Question:

a) Prove that ||B(x, y)|| = ||(x, y)|| for all (x, y) ˆˆ R2.
b) Let (x, y) ˆˆ R2 be a nonzero vector and Ï† represent the angle between B(x, y) and (x, y). Prove that cos Ï† = cos Î¸. Thus, show that B rotates R2 through an angle Î¸. (When Î¸ > 0, we shall call B counterclockwise rotation about the origin through the angle 0.)
Let