If the ellipse: [aleft(x^{2}-y^{2} ight)+2 b x y-frac{1}{2} omega_{o}left(x^{2}+y^{2} ight)+c=0] is full of liquid and is rotated

If the ellipse:

\[a\left(x^{2}-y^{2}\right)+2 b x y-\frac{1}{2} \omega_{o}\left(x^{2}+y^{2}\right)+c=0\]

is full of liquid and is rotated about the origin with an angular velocity, \(\omega_{o}\), the stream function is:

\[\psi=a\left(x^{2}-y^{2}\right)+2 b x y\]

a. What are the velocity components?

b. Is there any vorticity associated with this flow?