How much heat is needed to raise the temperature of 90g of water by 86oC

You would use the equation Q=cmΔT, where Q is the amount of heat added, c is the specific heat of the substance (or the amount of heat needed per unit of mass to raise the temperature by one degree Celsius), m is mass, and ΔT is the change in temperature. In this case, Q, heat added, would be equal to (1) (90) (86), which equals 7740 calories.