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Calculate the moments of inertia I1, I2, and I3, for a homogeneous cone of mass M whose height is h and whose base has a radius R. Choose the x3-axis along the axis of symmetry of the cone. Choose the origin at the apex of the cone, and calculate the elements of the inertia tensor. Then make a transformation such that the center of mass of the cone becomes the origin, and find the principal moments of inertia.

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