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The flux of a vector field $\vec{F}$ through a closed surface $S$ is 2. The surface $S$ consists of 4 faces $A$, $B$, $C$, and $D$.

If the flux through $A$, $B$, and $C$ are 1, $-4$, and 5, respectively, what is is the flux of $\vec{F}$ through $D$?

A

$4$

B

$0$

C

$-2$

D

$-4$

E

$-6$

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