A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by \(\mathbf{v}\) and the net is described by the given equations.

\(\mathbf{v}=\left\langle x-y, z+y+4, z^{2}ightangle\), net given by \(y=1-x^{2}-z^{2}, y \geq 0\), oriented in the positive \(y\)-direction