For each of the flows

(i) $\mathbf{u}=\left(2 x y, x^{2}+y^{2}\right)$

(ii) $\mathbf{u}=(-2 y,-2 x)$

determine whether or not the flow is incompressible and/or irrotational. Find the associated velocity potential and/or stream function when appropriate. For either one of the flows, sketch the streamlines of the flow, indicating the direction of the flow.