The prove of energy matter equivalence can be seen in nuclear reactions. The enormous energy released in an atomic blast is bound up in the matter before it causes such a fuss.
If you are asking why the letter c is used instead of another letter, I believe it is for celeritas the latin word for...
I can't be the only person to ever have this thought so I am hoping one of you star gazers can tell me what I am missing. I understand Hubble's theory and the idea of space itself expanding. My question is this. If we know the universe is expanding because of the redshift and the farther away we...
Good answer. I can't think of any interesting technical endeavor today that would be possible without complex numbers. Take communications and digital signals processing. Our electronic lives rely on the Fourier transforms and how fun would that be without using complex exponentials in
the...
It's not possible using integers. The bias that led to the name is inherent in that statement. Why are integers your measuring stick for "realness". Is pi not a real value. what about the distance across my square room corner to corner, is that not a real distance? It isn't rational. Imaginary...
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Hold on, I was confused by theta/phi ambiguity and your component ordering.
You have the correct spherical vector but in an unfamiliar order.
Since I typed all of this I will not leave it in case anybody else is helped by it.
What is p=rsinθ? the value of function f or the radial unit...
There are some important requirements to recall for electrostatics in conductors. For a conducting block there will be no electric field inside the conductor. The potential inside the block is the same everywhere, constant or zero difference. All the charge will be distributed on the surface...
By isolated do you mean not in the presence of an external electric field? Do you want net charge? On the surface, bound charges? The total charges on a microscopic scale would be the number of electrons and protons in the volume. isolated in no field the charge distribution is likely uniform as...
Personally I feel the choice of wording is unfortunate. Complex numbers are no more unreal than integers. Because they are called imaginary doesn't make Euler's any less fundamental. It's sad that somebody had to use real and imaginary to describe two sets of one fundamental tool of knowledge...
Fourier analysis transforms time domain signal into the frequency domain. There are several situations where it is invaluable like in digital signal processing for communications or image analysis, simplifying calculations such as transforming a difficult convolution in time into multiplication...
Are you trying to find the Fourier series representation or the Fourier transform of a periodic signal? In either case you don't need to deal with the absolute value. A rectified sine wave is a periodic signal with a period equal to half of the full sinusoid, I would write the sine in...
You didn't circle nodes. Those are corners. Nodes connect components, that is just a bend in a wire.
There are only two nodes on that outer loop that has the 12 and the 60. The center one is easy. Where is the 2nd node?
If the output is of the same form as the input but scaled by a constant is that an LTI system? Is the output the same form as the input? (coefficient of sin could be 0)
If it is time invariant the output you get from a time shifted input is the same as if you time shifted the output the same amount.
You have system H and its output y such that the system is described by y[n] = H{ x[n] },
if you shift input x1[n] so you get a new input x2[n] = x1[n-1] and you...