Problem 1 (Rotations). 1. Let [ be the rotation map in R? by 60 clockwise. Please compute the corresponding matriz and explicitly find f(x,y) for all (z,y) R2. 2. Assume v,w R? are orthogonal and f is the same function defined above. Explain why f(v), f(w) are also orthogonal. Hint: you do not have to compute the dot product. Problem 2 (Operations of Linear Transformations). 1. Let f:R R be a linear transformation and W C R be a linear subspace of R. We define the preimage of W under f to be W)= {veR": fv) e W} Prove that f~Y(W) is a linear subspace of R. 2. Given linear transformations f: R" R and g : R RP. Is the composition go [ : R" RP also a linear transformation? If so, please provide a proof. If not, please give a counterexample. Recall: the composition is defined to be (go f) (x) = g(f(x))