Consider the velocity field given by \(\vec{V}=A x^{2} \hat{i}+B x y \hat{j}\), where \(A=1 \mathrm{ft}^{-1} \cdot \mathrm{s}^{-1}, B=-2 \mathrm{ft}^{-1} \cdot \mathrm{s}^{-1}\), and the coordinates are measured in feet.

(a) Determine the fluid rotation.

(b) Evaluate the circulation about the "curve" bounded by \(y=0\), \(x=1, y=1\) and \(x=0\).

(c) Obtain an expression for the stream function.

(d) Plot several streamlines in the first quadrant.