The two ends of a straight line have coordinates (1,3) and (2,5). it is to be reflected about a straight line that passe: s through the points (0, 0.5) and (4, 6). write the necessary transformation matrix for the above operation, and determine the new coordinates of the end points of the line.

Apump is used to circulate hot water in a home heating system. water enters the well-insulated pump operating at steady state at a rate of 0.42 gal/min. the inlet pressure and temperature are 14.7 lbf/in.2, and 180°f, respectively; at the exit the pressure is 60 lbf/in.2 the pump requires 1/15 hp of power input. water can be modeled as an incompressible substance with constant density of 60.58 lb/ft3 and constant specific heat of 1 btu/lb or. neglecting kinetic and potential energy effects, determine the temperature change, in °r, as the water flows through the pump.

Give heat transfer applications for the following, (i) gas turbines (propulsion) ) gas turbines (power generation). (iii) steam turbines. (iv) combined heat and power (chp). (v) automotive engines

What is the heat treatment of metals? what is the benefit of it? why and how it's useful? answer in details, do not write by hand.