Determine by direct integration the product of inertia of the thin homogeneous triangular plate of mass m about the x-y axes. Then, use the parallel-axis theorem to determine the product of inertia for the plate about the x′-y' axes and the x″-y″ axes. What is the product of inertia about the centroid of the plate?

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y y, y" т h -b- -x, x' Thickness t