I appreciate any help with the following:

(1) A sinusoidal signal has an amplitude of 10, frequency of 2 Hz, and initial phase of 60 degrees. It passes through an LTI system and undergoes a gain of 3.5 and a 60-degree phase lag. The resulting output signal will be mathematically described as?

(2) A continuous time system has an output, y=4t^2 + 4, which is given by . It is sampled at a frequency of 8 Hz. Determine the expression that correctly represents the discrete signal obtained after sampling and its value for n = 4.

(3) A signal consists of only two sinusoids, one of 130 Hz and one of 245 Hz. This signal is sampled at a rate of 700 Hz. Find the first six positive frequencies that will be present in the replicated spectrum.

(4) A system samples a sinusoid of frequency 1,020 Hz at a rate of 670 Hz and writes the sampled signal to its output without further modification. Determine the frequency that the sampling system will generate in its output.

(5) Find the resolution of the Fourier transform if a signal is sampled at 16,384 samples/sec and we collect a total of 32,768 data points and then apply the FFT algorithm to all of them.