Choosing a server for hosting a web API
Can you help me with my capacity planning?
How to use "fit" to frame the nodes and labels I'm using the fit TikZ library to fit a rectangle around two nodes which include labels. However, the rectangle is only fit around the actual nodes, not about their labels:  \documentclass{article} \usepackage{tikz} \usetikzlibrary{fit}  \begin{document} \begin{tikzpicture}   \node [label=label1,draw] (node1) {Node1}; \node [label=label2,draw] (node2) at (4,2){Node2};  \node[fit=(node1)(node2), draw] {}; \end{tikzpicture} \end{document}     How to fit the rectangle also around the node labels? If $x+y+z=xyz$, prove $\frac{2x}{1-x^2}+\frac{2y}{1-y^2}+\frac{2z}{1-z^2}=\frac{2x}{1-x^2}\times\frac{2y}{1-y^2}\times\frac{2z}{1-z^2}$ given that $x^2~,~y^2~,~z^2\ne1$  I came across this question in an ancient ($19$th century) Trigonometry book, and this is the method they use to prove the result (please note: I understand this method fully): Let $x=\tan A$ ,$~y=\tan B$ and $z=\tan C$ which is acceptable without any loss of generality. This means that we are saying that $$\tan A+\tan B+\tan C=\tan A\tan B\tan C$$ Consider $\tan (A+B+C)$: $$\tan (A+B+C)=\frac{\tan A+\tan B+\tan C-\tan A\tan B\tan C}{1- \tan A \tan B- \tan C \tan A - \tan B \tan C}$$ So if $~\tan A+\tan B+\tan C=\tan A\tan B\tan C~~$ then $~~\tan (A+B+C)=0$. Hence, let $~A+B+C=\pi$. Now consider $\tan (2A+2B+2C)$: $$\tan (2A+2B+2C)=\frac{\tan 2A+\tan 2B+\tan 2C-\tan 2A\tan 2B\tan 2C}{1- \tan 2A \tan 2B- \tan 2C \tan 2A - \tan 2B \tan 2C}=0$$ $$\implies \tan 2A+\tan 2B+\tan 2C=\tan 2A\tan 2B\tan 2C$$ $$\implies \frac{2\tan A}{1-\tan^2 A}+\frac{2\tan B}{1-\tan^2 B}+\frac{2\tan C}{1-\tan^2 C}=\frac{2\tan A}{1-\tan^2 A}\times\frac{2\tan B}{1-\tan^2 B}\times\frac{2\tan C}{1-\tan^2 C}$$ $$\therefore\frac{2x}{1-x^2}+\frac{2y}{1-y^2}+\frac{2z}{1-z^2}=\frac{2x}{1-x^2}\times\frac{2y}{1-y^2}\times\frac{2z}{1-z^2}$$ as required.  My question is, is there any other way of proving this without this rather heavy use of trigonometry? I also would prefer not to work through heaps of algabraic manipulation and expansion to obtain the required result, although if that's necessary I will put up with it ;) Thank you for your help. How to calculate the rotation matrix between 2 3D triangles? I need to calculate the rotation matrix and the translation vector between 2 given triangles in Euclidean space.  This is really just a rotation and a translation, the lengths of sides of the triangle are equal.  Coordinates of the points are real. $P_1, P_2, P_3$ are the 3 points of the 1st triangle, $Q_1, Q_2, Q_3$ are the 3 points of the 2nd.  My idea was: I translate the center of the triangles to the point of origin with $t_1 := \frac{P_1+P_2+P_3}{3}$, $P'_i = P_i-t_1$ and  $t_2 := \frac{Q_1+Q_2+Q_3}{3}$, $Q'_i = Q_i-t_1$ and then I only need to solve the set of 9 linear equations with 9 unknown (the 9 entries of the rotation matrix $R$):  $$ Q'_i = R.P'_i $$ Afterwards I could calculate the translation with  $$ t = t_2 - R.t_1 $$ The problem is: after I translate the triangles to the point of origin the points are linearly dependent ($P_3 = -P_1 - P_2$)  So in fact I only have 6 equation with 9 unknown, which allows multiple solutions for $R$. But I need "one" precise solution, because the triangles are just parts of two identical models, which I need the rotation for.   I think the approach will work, if I use 4 points instead of 3.  But can I somehow calculate the rotation matrix with "only" 3 points? Ubuntu in VirtualBox wants to install on every boot A command-line clipboard copy and paste utility? In Windows I used command-line clipboard copy-and-paste utilities...      pclip.exe and gclip.exe     These were UnixUtils ports for Windows (but they only handled plain text). There were a couple of other native Windows utilities which could write/extract any format.    I've looked for something similar in Synaptic Package Manager, but I can't find anything.    Is there something there, that I've missed? ... or maybe this is available in Bash scripting?    The type of utility I'd like will be able to read/write via std-in/std-out or file-in/file-out, and handle Unicode, Rich Text Format, picture, etc. clipboard formats...    NB: I'm not after a clipboard manager. How can I blow out the background when shooting down for clothing on the ground? I'm using the Webform module for Drupal 8. The module confirmation settings for a form are the following:   Page (redirects to new page and displays the confirmation message) Inline (reloads the current page and replaces the webform with the confirmation message.) Message (reloads the current page/form and displays the confirmation message at the top of the page.) URL (redirects to a custom path or URL) URL with message (redirects to a custom path or URL and displays the confirmation message at the top of the page.)   But how am I able to submit a form via AJAX so that the page doesn't reload on submit, but a confirmation message still replaces the form? What did I do wrong?    EDIT:  Here is the solution which works:  First you have to hook the form alter function and set an AJAX callback (as in ):  use \Drupal\Core\Form\FormStateInterface;  function MYTHEME_form_alter(&amp;$form, FormStateInterface $form_state, $form_id) {   if ( isset($form['#webform_id']) &amp;&amp; $form['#webform_id'] == 'MYWEBFORM' )   {     // add an AJAX callback to the form submission     $form['actions']['submit']['#ajax'] = array(       'callback' =&gt; '\Drupal\MYMODULE\Controller\DefaultController::processFormSubmission',       'event' =&gt; 'click',     );   } }   Then in the processFormSubmission function you can process the form (put use \Drupal\Core\Form\FormStateInterface; at the top of your file) like:  // Instantiate an AjaxResponse Object to return. $ajax_response = new \Drupal\Core\Ajax\AjaxResponse();  /* do sth */  // in the DOM: replace the form with the text 'form submitted' $ajax_response-&gt;addCommand(new \Drupal\Core\Ajax\HtmlCommand('#MYFORM', 'form submitted'));  return $ajax_response; Not able to install Win Xp on Lenovo Ideapad z570 I want to install Win Xp on my Ideapad Z 570 laptop but i always get blue screen with message with some drive related problem which asks me to run CHKDSK command. I tried with that but no luck. Is there any way i can install Win Xp with SP 2 ?  Edit: i searched across the sites and came to know there could be some Compatibility problems, and i could fix it by setting HDD mode to IDE; will it solve the problem? How are the best director award winners chosen? I do not understand how the best director awards are determined each year. It seems impossible to assess the method of a movie director unless you are part of the crew.  So, how do the nominators/judges assess the directors' performance each year? Sensitivity to initial conditions and topological transitivity If space of bounded operators L(V,W) is Banach, V nonzero, then W is Banach (note direction of implication) Let $V,W$ be normed vector spaces, and $L(V,W)$ be the space of bounded linear operators. Usually I would only see the statement "If $W$ is Banach, then $L(V,W)$ is Banach.". But  writes that there is a converse: "If $L(V,W)$ is Banach, and if $V$ is non-trivial, then $W$ is Banach". This is pretty interesting since I never seen a converse before. I was wondering if anyone has a nice proof.  I tried reversing the proof for the usual direction, but the inequalities can't be reversed. I also tried to start with a Cauchy sequence in $W$, and construct linear operators (using Hahn-Banach to control the operator norms), but alas I cannot say much about the distance between these operators (much less say that it is Cauchy) How to factor intricate polynomial $ ab^3 - a^3b + a^3c -ac^3 +bc^3 - b^3c $ I would like to know how to factor the following polynomial.  $$ ab^3 - a^3b + a^3c -ac^3 +bc^3 - b^3c $$ What is the method I should use to factor it? If anyone could help.. Thanks in advance. Root filesystem check fails after power failure during installation During the "install" phase of the upgrade there was a power failure. After when starting up again the following errors are reported:  init: udevtrigger main process (420) terminated with status 1 init: udevtrigger post-stop process (428) terminated with status 1 init: udevmonitor main process (419) killed by TERM signal The disk drive for / is not ready yet or not present Continue to wait; or press S to skip mounting or M for manual recovery   Pressing M gives me the following message:  Root filesystem check failed. A maintenance shell will now be started. CONTROL-D will terminate this shell and reboot the system. Justify text inside itemize environment with beamer class I would like a way to convert a document from HTML to LaTeX on a Windows platform. What is my best option? Do neutrinos not couple to the Higgs field? Stack Exchange API too many requests from this IP address I am using the Stack Exchange API to get Stack&nbsp;Overflow data, but I am getting "too many request from this ip" after making only five requests. I got JSON content like this:  {u'error_id': 502, u'error_message': u'too many requests from this IP, more requests available in 68492 seconds', u'error_name': u'throttle_violation'}   I made the following requests to Stack&nbsp;Exchange without an access token:   "" ---> 2 times called this API "" --> 3 times called this API and on the 4th call I got an exception Must I enter Europe with Schengen visa from the country where I applied? If I applied for a Schengen visa from "country A" and I got the visa but I had some commitments in "country B" and I have to finish it before going to Europe should I get back to "country A" to travel to Europe or can I use the visa from any where? Silencing "Your disk is almost full" notification How many passes do you need to wipe/shred your files to make them not undeletable?