1. (5 marks) Determine whether each statement is true or false. Justify your answer. (a) (1 mark) The vector field F(x, y) = (-y, x) is conservative on R. (b) (1 mark) If f : IR' - R is C' then ( Vf . dr = 0 where C is the ellipse # + # = 1. (c) (1 mark) The length of the parametric curver(t) = (-2 + 4 cos(t ), 3 + 4 sin(t) ), te [0, ~] is 47. (d) (1 mark) The Jacobian of the transformation (x, y) = T(u, v) = (utv, u - v) is 2