= Solution
The antisymmetric velocity-gradient tensor $\boldsymbol\Omega$ is the local angular velocity of a rigid-body rotation. Under such a rotation a material vector must rotate at exactly the same angular velocity, independently of its molecular constitution. The coefficient of $\boldsymbol\Omega\mathbin{\cdot}\mathbf p$ is therefore fixed to one by rotational covariance, also called material objectivity. In contrast, the symmetric strain-rate tensor $\mathbf D$ deforms rather than merely rotates the material, so its flow-alignment coefficient $\xi$ is material dependent.
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