Draw line with markers in WPF Canvas
Graph nodes coordinates evaluation
I'd like to output hello world over 20 characters.  printf "%-20s :\n\n" 'hello world!!'  # Actual output hello world!!        :  # Wanted output hello world!!========:   However, I don't want to complete with spaces but with "=" instead. How do I do that? Watching The Lord of the Rings movies I was really captivated by the   elephant riders and the men in brazen scale armor who aided the orcs   against the forces of Gondor and Rohan. From what I know they are from   the cultures that worship Sauron. I'd like to know what Tolkien wrote   about them, their religion, their way of life, and so on.   From The sup norm on $C[0,1]$ is not equivalent to another one, induced by some inner product Let $\mathrm{C}[0,1]$ be the space of continuous functions $[0,1]\rightarrow \mathbb{R}$ endowed with the norm $||x||_{\infty}=\mathrm{max}_{t\in [0,1]}|x(t)|$. It is easy to verify that this norm is not induced by any inner product (really the parallelogram law fails for $x(t)=t$ and $y(t)=1$). Well, how to understand that this norm is not equivalent to anyone induced by an inner product? So, the norms induced by inner products should have some special properties... Assuming I'm paying long term capital gains tax, what is the break even point where it is more worthwhile to switch from one fund to another?  For (a hypothetical) example, if I have a fund with an expected return of 3.5%, what would be the minimum expected return of another fund to make it worthwhile to pay the capital gains tax and switch to the other fund?  (I'm assuming the answer to this question is an equation involving investment horizon, capital gains tax rate, and my current taxable gains) Do new wire runs in an existing ceiling need to be stapled down? I've heard some people say that code requires wiring in the wall to be stapled to framing every so often (how often?), but when you are doing a remodel, is that necessary?  I have a two story house, and would like to remove one standard dome light on the first floor ceiling and replace it with 6 recessed lights.  There is about 12" of empty space between the floors, and it seems easy enough to run the wire from light to light without cutting any drywall except for the 4-5" holes required for the lights. However, there's no way I'd be able to staple the wiring down.  It's just going to be loose in the ceiling, running through a small hole in the I joists every once in a while.  They sell "remodel" light cans that are made specifically so you only have to cut a hole big enough for them to fit in, so this seems like a common job.  What am I missing and how can I do this job in the most correct way?  This is in Dallas, TX, single family residence. limit of the sequence $a_n=1+\frac{1}{a_{n-1}}$ and $a_1=1$ Terminal only shows up as a black window What is a decoupling capacitor and how do I know if I need one? What is a decoupling capacitor (or smoothing capacitor as referred to in the link below)?  How do I know if I need one and if so, what size and where it needs to go?    mentions many chips needing one between VCC and GND; how do I know if a specific chip is one?   Would an  4-bit parallel access shift register used with an Arduino need one? (To use my current project as an example) Why or why not?  I feel like I'm starting to understand the basics of resistors and some places they're used, what values should be used in said places, etc, and I'd like to understand capacitors at the basic level as well. what is the real use case of dependency injection? Let $A,B$ be real symmetric matrices, and for any $n\in \Bbb N^{+}$, and for all $x,y\in \Bbb R$, we have $$tr(xA+yB)^n=x^ntr(A^n)+y^ntr(B^n).$$  Show that $AB=0$.  My try:since $$(xA+yB)^n=x^nA^n+\binom{n}{1}x^{n-1}A^{n-1}yB+\cdots+\binom{n}{n-1}xA(yB)^{n-1}+y^nB^n$$ so $$tr\left(x^nA^n+\binom{n}{1}x^{n-1}A^{n-1}yB+\cdots+\binom{n}{n-1}xA(yB)^{n-1}+y^nB^n\right)=x^ntr(A^n)+y^ntr(B^n)$$  then  $$tr\left(\binom{n}{1}x^{n-1}A^{n-1}yB+\cdots+\binom{n}{n-1}xA(yB)^{n-1}\right)=0$$ so $$\binom{n}{1}x^{n-1}ytr(A^{n-1}B)+\cdots+\binom{n}{n-1}xy^{n-1}tr(AB^{n-1})=0$$ then I can't  I found this is a nice result, maybe this is an odd problem, and I can't solve it. Thank you. Is there a way to transfer more than one Pokemon at a time? Is there a way to transfer more than one Pokemon at a time to the professor?  Or possibly an addon that gives me this ability?  Vendoring all the trash Pokemon for candies individually is really annoying and time consuming. Display date/time in user's locale format and time offset I want the server to always serve dates in UTC in the HTML, and have JavaScript on the client site convert it to the user's local timezone.  Bonus if I can output in the user's locale date format. Is there an intelligent way to left-align the parts right of &amp; of the two cases environments shown below (if x >= 0, otherwise, if y &lt; 0, otherwise). I wonder if there is a better way than using manual spaces:  \begin{align*}  u(x) &amp;=   \begin{cases}    0        &amp; \text{if } x \geq 0 \\    1        &amp; \text{otherwise}   \end{cases}   \\  \tau &amp;=   \begin{cases}    a+b+c+d  &amp; \text{if } y &lt; 0 \\    1        &amp; \text{otherwise}   \end{cases} \end{align*} I'm trying to transition from a list of pros to a list of cons, and would like to have some sort of transition quote. Something in the form of,  "But, alas, (((something something quote quote)))"  Everything that has a beginning has an end, something along the lines of that. In superluminal phase velocities, what is it that is traveling faster than light? I understand that information cannot be transmitted at a velocity greater than speed of light. I think of this in terms of the radio broadcast: the station sends out carrier frequencies $\omega_c$ but the actual content is carried in the modulated wave, the sidebands $\omega_c\pm\omega_m$. The modulation envelop has its group velocity and this is the speed at which information is being transmitted. We also know, for example, that x-rays in glass have a phase velocity which is greater than the speed of light in vacuum.   My question is, what exactly is it that is travelling faster than the speed of light?    EDIT: I know it couldn't be anything physical as its superluminal. My problem is, what is it that has absolutely no information content yet we associate a velocity with it. Avoid if for chained objects Which of these two phrases has more negative undertone?      "The interview I had was not very good"    or      "The interview I had was not good" Make Bash autocomplete guess the closest approximation I have a somewhat uncomfortable keyboard on my laptop, resulting in that I sometimes misspell things in Bash and when pressing Tab for an auto-completion nothing happens.   Is it possible to have Bash guess what I meant to type, by for example when wanting to change directory to Documents and then mistyping cd ocum[TAB], given no other folder beginning with "ocum" is present, Bash interprets it as cd Documents/ since it is the closest possible action to do?   Or is this idea terribly complicated to achieve? Atmospheric pressure experiment using a cup with a fluid to hold a glass plate When I was in high school, my teacher did an experiment to show the power of atmospheric pressure.  Experiment: Prepare a glass bottle, fill with water, put a glass plate on the bottle, make sure there is no air in the bottle, just water. Hold the glass bottle and plate, and invert them. Slowly, release the hand which hold the plate. Because the atmospheric pressure, the glass plate will not fall down.    Question 1: As we know, if we didn't put water into the glass bottle, just air in the glass bottle the glass plate will fall down. So, If we use other liquid instead of water, this liquid has smaller density than water, like alcohol, the plate will not fall down. But, if we continue to chose the smaller density liquid until the liquid has density like air the plate will fall down. So, if there is a threshold density of liquid make the plate between falling  down and not falling down?  Question 2: If we put the bottle and plate into water slowly, when the plate and part of bottle are in the water but part of the bottle still above the water, will the plate fall down?  Question 3: Continuing question 2, when both bottle and plate are in the water I know the plate will fall down. So, how does the pressure of water and atmosphere change?  Is there a good description of this phenomena?  Why does the trick continue to work with lower density fluids and why does placing the plate in the water cause it to fall? Do you "gain" your 1st level?