Let $\sigma$ be unit cube where each face is parameterized so that the unit normal vectors point outwards. For the vector field $F = x{\bf k}$ determine if the flux across the face is positive, negative, or zero:
The flux across the face $x = 0$ is ? positive negative zero
The flux across the face $x = 1$ is ? positive negative zero
The flux across the face $y = 0$ is ? positive negative zero
The flux across the face $y = 1$ is ? positive negative zero
The flux across the face $z = 0$ is ? positive negative zero
The flux across the face $z = 1$ is ? positive negative zero