Create a matrix that represents the following transformation
T_center ((x, y, z)ᵀ) = (x - Cₓz, y - Cᵧz, z),
where Cₓ, Cᵧ are the coordinates of the center found in the previous part. i. e. Translation in the y-direction by one unit. You can test that you have the correct matrix by applying the transformation (multiplying the transformation matrix) to each column in the matrix of homogeneous coordinates and then plotting the new points using the plot points() function from above. Use a for-loop to apply this transformation.

Amass of m 1.5 kg of steam is contained in a closed rigid container. initially the pressure and temperature of the steam are: p 1.5 mpa and t 240°c (superheated state), respectively. then the temperature drops to t2= 100°c as the result of heat transfer to the surroundings. determine: a) quality of the steam at the end of the process, b) heat transfer with the surroundings. for: p1.5 mpa and t 240°c: enthalpy of superheated vapour is 2900 kj/kg, specific volume of superheated vapour is 0. 1483 m/kg, while for t 100°c: enthalpy of saturated liquid water is 419kj/kg, specific volume of saturated liquid water is 0.001043m/kg, enthalpy of saturated vapour is 2676 kj/kg, specific volume of saturated vapour is 1.672 m/kg and pressure is 0.1 mpa.

Awall of 0.5m thickness is to be constructed from a material which has average thermal conductivity of 1.4 w/mk. the wall is to be insulated with a material having an average thermal conductivity of 0.35 w/mk so that heat loss per square meter shall not exceed 1450 w. assume inner wall surface temperature of 1200°c and outer surface temperature of the insulation to be 15°c. calculate the thickness of insulation required.

How much power could a wind turbine produce if it had the following specifications? cp = 0.45 -d=1.2kg/m3 d=50m v 5m/s