Fourier transform review (a) consider two vectors in the plane: 4%p, v2/2 -v2/2 v2 for an arbitrary vector x, specify scalars a and a so that (hint: inner product.) b) make a sketch corresponding to part (a). (c) view the three blue one brown fouier video (d) give an interpretation of the fourier transform based on part (a) above. note that for square-integrable complex-valued functions f(t) and g(t), the inner product is given by (f, s) = | f. (t)g(t)dt. (e) compare and contrast the interpreation in the video to the interpretation in part (d)

Manometers are good examples of measuring instruments, nowadays they are not as common as before. a)-capacitive probe gauges b)-gravitational gauges deformation ) gauges d)-digital gauges

A3-mm-thick panel of aluminum alloy (k 177 w/m-k, c 875 j/kg-k and ? = 2770 kg/m) is finished on both sides with an epoxy coating that must be cured at or above t,-150°c for at least 5 min. the production line for the curing operation involves two steps: (1) heating in a large oven with air at ts,0-175°c and a convection coefficient of h, 40 w/m2. k, and (2) cooling in a large chamber with air at 25°c and a con- vection coefficient of he 10 w/m2.k. the heating portion of the process is conducted over a time interval te which exceeds the ime required to reach 150°c by 5 min (h = r + 300 s). the coating has an emissivity of ? = 0.8, and the temperatures of the oven and chamber walls are 175 and 25°c, respectively. if the panel is placed in the oven at an initial temperature of 25°c and removed from the chamber at a safe-to-touch tempera ture of 37°c, what is the total elapsed time for the two-step curing operation?

10 kg of co2 is initially contained at 400 kpa and 300 k. the gas constant for carbon dioxide is 189 j/lkg k) and has a specific heat ratio, k, of 1.289. isentropic expansion then occurs until the pressure is 200 kpa. a) determine the initial volume of co2 in m. b) determine the final temperature in k. c) determine the work done by the system during the expansion kl.