1. A hemispherical bowl of radius 2 m lies with its base on the xy-plane and with its center at the origin. Write the expression for the scalar field, describing the height of points on the bowl as a function of x and y.
2. A number equal to the sum of its coordinates is assigned to each point in a rectangular room having three of its contiguous edges as the coordinate axes. Draw a sketch of the constant-magnitude surfaces for the number field generated in this manner.