Center of Mass: The coordinates of the center of mass are = My M and MT y= M' where M is the total mass, My is the moment around the y-axis, and M is the moment around the x-axis. M = R = √(x, y) dr dy R M₂ = √ √₂vo (x, y) dx dy My = R √xo o(x, y) dx dy 1. Find the center of mass of a two-dimensional plate that occupies the square [0, 1] x [0, 1] and has density function 8(x, y) = xy. 2. Find the center of mass of a two-dimensional plate that occupies the upper unit semicircle centered at (0,0) and has density function d(x, y) = y.