If \[ \overline{F}=(2x^{2}-3z)\mathbf{i}-2xy\mathbf{j}-4x\mathbf{k}, \] then \[ \int_{V}\nabla\cdot\overline{F}\,dV=\_ \] where \(V\) is the closed region bounded by \[ x=0,\quad y=0,\quad z=0,\quad \text{and}\quad x+2y+z=4. \]
The circulation of \(\vec{F}=y\hat{i}+z\hat{j}+x\hat{k}\) around the circle \(x^2+y^2=1,\ z=0\) is ____.