How can place an element at the bottom of another element using CSS?
How to align content of a div to the bottom
How to show that $\sum_{k=1}^n k(n+1-k)=\binom{n+2}3$? Matrices - Conditions for $AB+BA=0$ The Problem Let $A$ be the matrix $\bigl(\begin{smallmatrix}a&amp;b\\c&amp;d\end{smallmatrix} \bigr)$, where no one of $a,b,c,d$ is $0$. Let $B$ be a $2\times 2$ matrix such that $AB+BA=\bigl(\begin{smallmatrix} 0&amp;0\\ 0&amp;0 \end{smallmatrix} \bigr)$. Show that either   $a+d=0$, in which case the general solution for $B$ depends on 2 parameters, or $ad-bc=0$, in which case the general solution for $B$ depends on one parameter.   (this is question 22 of the last matrix exercise of Further Pure Mathematics by Bostock et al.)  Comments Writing $B=\bigl(\begin{smallmatrix} e&amp;f\\ g&amp;h \end{smallmatrix} \bigr)$ and multiplying out I get that    $(a+d)(f+g)+(b+c)(e+h)=0$ $ae+bg+cf+dh=0$   but I am unable to get the required restrictions on $a,b,c,d$. Is there a quick way of doing the problem that doesn't require manual computation? I thought of considering invertible and non-invertible cases but couldn't get anywhere. Help would be much appreciated. How and why do normalization and feature scaling work? I see that lots of machine learning algorithms work better with mean cancellation and covariance equalization. For example, Neural Networks tend to converge faster, and K-Means generally gives better clustering with pre-processed features. I do not see the intuition behind these pre-processing steps lead to improved performance. Can someone explain this me? Is there any way of doing something like,  &lt;script runat=server&gt;     Platform.Load("core","1");     //initialize DE     var _Sent = DataExtension.Init("_Sent");     //retrieve data     var _Sent_data = _Sent.Rows.Retrieve();     Write("Length: " + _Sent_data.length); //returns 0 &lt;/script&gt;   What would the external key for a system dataview be? I have a PDF with 100 pages. How can I make a new PDF that displays 4 pages on one?  I know that I can do it with Chrome by printing the PDF to new PDF and change this in the options. But I want to make it for a lot of files and put it as a script. Inductive proof of the closed formula for the Fibonacci sequence Where did Harry's parents get all of their money from? In English, the number 0 is treated as plural. It is then:   0 seconds 1 second    1.2 seconds   2 seconds     Shouldn't it be "nobody want to go there," instead of "nobody wants to go there"?  I also saw in TOEFL that "any __" should be used with a singular.  But I see it very common that it is a plural also.  Why is that?  (updated: example, "we don't have any apples any more" vs "If you get any apple, please let me know.") How to securely delete files stored on a SSD? How can I make my browser lie about my operating system? I'm using Chromium (Version 30.0.1599.114 Ubuntu 12.10) under Linux. I'm trying to access  that claims that it doesn't work under Linux. Of course, this is most likely crazy since the web is platform-independent (unless they're using some kind of evil plug-in).  I've used a user agent switcher to supply a Windows user agent, but to no avail. Upon viewing the source, it appears that the site is using Javascript to determine the operating system. I'm looking for a way to get my browser to report in Javascript that it is Windows or MacOS.  Do you know how to do it? Consider the sequence $(\phi_n)_{n\in \mathbb{N}}$ of test-functions $\phi_n\in \mathcal{D}(\mathbb{R})$ defined by  $$\phi_n(x) = \dfrac{n}{\sqrt{\pi}}e^{-n^2x^2}.$$  I want to show that this is a delta sequence, in the sense that:  $$\lim_{n\to\infty}(\phi_n,\psi)=(\delta,\psi)=\psi(0), \quad \forall \psi\in \mathcal{D}(\mathbb{R}).$$  In that case we know that we have  $$(\phi_n,\psi)=\dfrac{n}{\sqrt{\pi}}\int_{-\infty}^{\infty}e^{-n^2x^2}\psi(x)dx.$$  The problem here is to compute this integral. The function $x\mapsto e^{-n^2x^2}\psi(x)$ has no singularities, hence contour integration wouldn't help. Integration by parts or substitution also doesn't seem to be of great help.  The major problem is that there is a function $\psi$ inside the integral about which we don't know really anything apart from the fact that it is $C^\infty$ and with compact support.  How can we compute this integral and in the end show that the sequence $(\phi_n)$ is a delta sequence?  Just to make clear, I'm here doing all of this in the context of the Riemann integral. How to access blocked sites? I am in Pakistan and  is blocked here. I want to take the Lecture videos from YouTube. In Windows, I was using  to bypass the proxy.   But now, using Ubuntu, I don't know how to bypass the proxy. I found some where that i can bypass the proxy by using putty software. Can you guide me how can I bypass proxy by that? I tried, but I was not able to do so. Kindly tell me some easy method to bypass proxy. I don't want to used websites like accesstoblockedsites.com. Does there exist a free good molecule / atom simulation software? I'm looking for a software or software package (for example C/C++) that can simulate a lot (say thousands at least) of molecules in action (ie. in movement or attached to say static walls).  I have found several but they seems to be either 'gas only', 'water only', or not really scientific (a lot of small balls dodging around moved by an unique formula). Javascript multiple replace Why is Harry Potter a half-blood? Find lines from a file which are not present in another file Use nmcli to modify VPN password? With nmcli, I can modify VPN data like this:  nmcli con modify myvpn vpn.data 'refuse-pap = yes, user = xxx'   So I'm wondering if I can set password this way as well? I am preparing a document in French, using the "babel" package with option "french" and using commands that include colons and semicolons. My problem is, the French spacing before colons and semicolons disappears when the commands are printed. I do not understand why, have not been able to find an answer. Below is a MWE.  \documentclass{article} \usepackage[french]{babel} \newcommand\deuxpoints{Texte: texte} \begin{document} \deuxpoints\ \endgraf Texte: texte \end{document} Evaluation of $\int\frac{1}{x^2.(x^4+1)^{\frac{3}{4}}}dx$ Changing parameter values according to other parameter choice in Processing script using QGIS 3?