In a mixing bowl, combine the first five ingredients. Add the water, oil, vinegar, and vanilla. Beat on low speed for 1 minute. Beat on medium speed for 1 minute. Pour into a greased 13 X 9 baking pan. Bake at 350 degrees for 40-45 minutes or until toothpick comes out clean. Cool on a wire rack.
For frosting, in a mixing bowl, beat the milk and pudding mix for 2 minutes. Beat in whipped topping and spread over cake. Refrigerate leftovers.