A. it is believed that various constituents of the universe (radiation, matter and cosmological constant) provided the dominant contribution to the energy density at different times over cosmic history. in this part of the question, which considers this issue, r(t) is the scale factor at cosmic time t, and to is the present time. you can assume that the age of the universe is 13.7 billion years. also, assume th be the time at which the universe changed from being radiation-dominated to matter-dominated. i. u estimate r(t1) r(to). ii. given that the current temperature of the background radiation is 2.73 k, calculate the temperature of the radiation at t1. ili. calculate t1 using a relationship between cosmic time and temperature for the early universe and your answer from part (a)(ii). express your answer in years

Fft review: linspace, fs, fftshift, nfft 1. generate one second of a cosine of w,-10hz sampled at f, = 100hz and assign it to x. define a tt as your time axis 2. take 64 points fft. 3. as you remember, the dft (which the fft implements) computes n samples of s2t where k-0,1,2, n -1. plot the magnitude of this 64-points fft at range 0 to 63, what do you think of this graph? 4â·to get the x-axis into a hz-frequency form, plot this 64-points fft between-50 to 50 (the 100hz sampling rate) and have n-points between them. 5. according to your figure, what frequency is this cosine wave at? 6. remember that the fft is evaluating from 0 to 2ď€. we are used to viewing graphs from-ď€ to ď€. therefore, you need to shift your graph. 7. now according to your shifted graph. what frequency is this at? 8. note that the spikes have long drop-offs? try a 1024-point dft. note that the peak is closer to 10 and the drop-off is quicker. although, now sidelobes are an issue

Explain what it means to view something from a frame of reference. provide an example that illustrates your explanation. (4 points)

1kg of water needs to recieve 4200j of energy to go from 90 degrees to 91 degrees. what is the specific heat capacity of water? what are the units?