Question 3: Simulating heat diffusion (5 points) Let u(x, y,t) denote the temperature of an object at the location (x, y) in the plane and at time t. This function will change over time as heat spreads throughout space, and the heat equation is used to determine the change in the function u(x, y,r) over time. The two dimensional heat equation is: Intuitively, the heat equation says that the rate of change of the temperature is proportional to the 'curvature" of the object. The sharper the transition in u(x, y, r), as measured by the right hand side of the heat equation, the faster the temperature will change in time (which is the left hand side). We are going to simulate heat diffusion on a hot plate. If our intuition is correct, we would expect the heat to diffuse fastest at the edge of the plate, and slowest in the center. Let's see what happens! Part 1: Creating a hot plate in Python (2 points) First we need to create a hot plate, in Python. To do so, we are going to create a two dimensional box, and put the hot plate in the center of it. To that end, create a function make hotplate that takes the following inputs: W: The width of the box (in cm) h: The height of the box (in cm) r: The radius of the hot plate (in cm) Teoo1: The ambient temperature in the box, not of the plate in Farenheit) Thot : The temperature of the plate in Farenheit) The function should return a 2D numpy array that represents the plate in the center of the box. You should sample the box every cm along the horizontal and every y along the vertical. For simplicity, you may assume that x-y-0.1 cm throughout this question. Use the function imshow in matplotlib to display your hot plate, and make sure your visualization has a colorbar and that you use the colormap 'hot