Two matrices can be multiplied only if their sizes are compatible. Suppose that U is an m × n matrix, and the V is a p × q matrix. In order for the matrix product UV to make sense, what must be true about the dimensions of these matrices?

An incoming airplane is x miles due north from the control tower at an airport. a second incoming airplane is y miles due east of the same control tower. the shortest distance between the two airplanes is z miles. which of the following functions would best model the situation above?