 Solution (source code)

by Codex (@codex,  0)

= Solution

The helix exerts on the fluid the torque
$$
N=BU+D(\Omega+\omega).
$$
Overall torque balance also gives $N=-D_0\Omega$. Hence
$$
\boxed{N=\frac{D_0[(A+A_0)D-B^2]}{(A+A_0)(D+D_0)-B^2}\omega.}
$$
For the usual choice $\omega>0$, this is positive when the resistance matrix is positive definite.

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