# All Questions

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### bird traveling to a nest wants to save energy

This is a multiple choice question in one of tests I just wrote and I did not know the answer to it. I was just stuck on this during the test. It is a very weird question, one I find to be impossible. ...
296 views

### Is the diagonal morphism always a monomorphism?

What properties of a category have to be fulfilled such that every diagonal $\Delta:X\to X\times X$ is a monomorphism? Is this true for ''reasonable'' categories?
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156 views

### Calculating dB output from this example

This is my extra credit assignment so don't tell me answers, but please guide me how I should do this. I need to learn. Question states: Determine the power output of the receiver in watts and in the ...
112 views

### Rewriting a matrix as a polynomial

If a finite dimensional matrix $A$ is positive semidefinite, how can we write $A$ as a polynomial in $A^{2}$? Thanks.
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### Identifying quotient rings of product rings

Given two rings $R,S$ and a principal ideal $((a,b))=I\in R\times S$ where $(a,b)\in R \times S$; is it true in general that $(R\times S) / ((a,b))\cong R/(a)\times S/(b)$?
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### Definition of Compact Mapping

I was reading around the other day and came across the term "compact mapping". After googling, I saw the following two definitions: Let $X$ be a topological space. Then a mapping $f:X \to X$ is ...
### One-to-one mapping from $\mathbb{R}^4$ to $\mathbb{R}^3$
I'm trying to define a mapping from $\mathbb{R}^4$ into $\mathbb{R}^3$ that takes the flat torus to a torus of revolution. Where the flat torus is defined by \$x(u,v) = (\cos u, \sin u, \cos v, \sin ...