What is the purpose of control group ?

What are the phases shown in a and d called?

Find the dimensions and area of the largest rectangle that can be inscribed in the upper half of the ellipse. (give your answers in terms of a and b. enter the dimensions as a comma-separated list.)

An insulated thermos contains 148 g of water at 72.7 ˚c. you put in a 11.7 g ice cube at 0.00 ˚c to form a system of ice + original water. the specific heat of liquid water is 4190 j/kg•k; and the heat of fusion of water is 333 kj/kg. what is the net entropy change of the system from then until the system reaches the final (equilibrium) temperature?