(a) (b) Define the rotation operator of any vector (x, y) in IR2 through an angle...

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(a) (b) Define the rotation operator of any vector (x, y) in IR2 through an angle 0 and find the image of the vector (3, 1) under a rotation of /3 radiun about the origin. Determine whether the transformation T(x,y) = (x, y) is linear. (c) Determine whether the linear operator T: R2 R2 defined by the equations ->> (a) (b) Define the rotation operator of any vector (x, y) in IR2 through an angle 0 and find the image of the vector (3, 1) under a rotation of /3 radiun about the origin. Determine whether the transformation T(x,y) = (x, y) is linear. (c) Determine whether the linear operator T: R2 R2 defined by the equations ->>