Question 2. ( 12 points) (a) A thin plate of constant density p(x, y) = 1 is to occupy the trian- gular region in the first quadrant of the xy-plane having vertices (0, 0), (a, 0) and (a, !). What value of a will minimize the plate's moment of inertia about the origin? (b) i) Find the centroid of the plane region defined by the polar coordinate inequalities 0