4. (a) Let T : R2 -> R2 be rotation by 7/3, i.e. T(x) = the rotation of x by 7/3 around 0. From your answer to 3(f), without computing any matrices, what would you expect det(A) to be? (Does T make areas larger or smaller?) Guess, then check using the fact that the matrix for rotation by 0 is A = cos(0 - sin(0) sin(0) cos(0) Bonus: explain why this is the matrix for rotation by 0. (b) If T : R2 -> R2 is rotation by angle 0, what is det(A)? Does this make sense in terms of areas