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1. Find the center of mass of the upper half of the sphere of radius a with center at the origin and (x, y, z) = 1.

2. A triangular plate bounded by the lines x = 0, x = y, y = 1 has density (x, y) = x + y. Find the moments and center of mass.

3. Find the moment of inertia with respect to y-axis of a triangular lamina with vertices (0,0), (1,0), and (0,2) of the density function is (x, y) = 1 + 3x + y.