A motorboat, which has a speed of 8.0 meters per second in still water, is headed east as it crosses a river flowing south at 3 meters per second. What is the magnitude of the boat’s resultant velocity with respect to the starting point?

The key to stability is feedback between the reservoir and the fluxes into and/or out of the reservoir. assume that the rate of outflow from a reservoir depends on the size of the reservoir according to the following relationship: outflow rate= k x (size of reservoir), where k is a constant. a reservoir of water has a volume of 5000 liters, and the rate of outflow at steady state is 25 liters per minute. what is k? (give both the numerical value and its units.) what is the residence time? what is the relationship between k and the residence time?

Acylinder with a movable piston contains 11.7 moles of a monatomic ideal gas at a pressure of 1.32×10^5 pa. the gas is initially at a temperature of 300 k. an electric heater adds 43200 j of energy into the gas while the piston moves in such a way that the pressure remains constant. cp=20.79 j k^−1 mol^−1 for a monatomic ideal gas, and that the number of gas molecules is equal to avogadro's number (6.022×10^23) times the number of moles of the gas. (a) what is the temperature of the gas after the energy is added? (b) what is the change in volume of the gas? (c) how much work is done by the gas during this process?

Point charges q1=+2.00μc and q2=−2.00μc are placed at adjacent corners of a square for which the length of each side is 1.50 cm . point a is at the center of the square, and point b is at the empty corner closest to q2. take the electric potential to be zero at a distance far from both charges. part a what is the electric potential at point a due to q1 and q2? express your answer with the appropriate units.