5. Consider the domain ID) = {(23, y) : 3:2 + y2 0} in the (u, 1)) plane to ID) in the (3:,y) plane given by: u2+v21 a:=, u2+('u+1)2 _ 2u y_ u2+(v+1)2' 1 Write u and v in terms of 33 and y. Your answers here should be rational functions in a: and 3;. That means no roots. Call this new change of coordinates C" 1 . Write u and v in terms of a: and 3;. Your answers here should be rational functions in a: and 3;. That means no roots. Call this new change of coordinates 01. (ii) Consider the domain T depicted below bounded by the curves: (ac1)2+(y~/3)2=3 (a: + 2)2 + y2 = 3 (m1)2+(y+\\/)2=3 Use your answer in part (i) to compute C '1 (T) (Draw a picture). (ii-i) Compute |det(C)I and ldet(C-1) l (is) Compute 4 if (1 :2 [$me by changing to (u, v) coordinates. Figure 1: Domain T