= Solution
The power supplied to overcome drag equals the <viscous dissipation>:
$$
-\mathbf F\cdot\mathbf U
=2\mu\int_{\mathcal D}\mathbf e:\mathbf e\,dV,
\qquad
\mathbf e=\frac12\left(\nabla\mathbf u+\nabla\mathbf u^T\right).
$$
For a nonzero rigid translation the strain cannot vanish throughout a fluid at rest at infinity, so the integral is strictly positive. Since $\mathbf F=-\mathbf R\mathbf U$,
$$
\boxed{\mathbf U\cdot\mathbf R\mathbf U>0
\quad\text{for every }\mathbf U\ne0}.
$$
\b[Thus the symmetric resistance matrix is <positive-definite matrix>[positive definite].]
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