Sir $P=F/A$ And since $F$ and $A$ both are vectors but $P$ is scalar. So doesn't it violates that &quot;Division is NOT defined for vectors&quot;?
Can we divide two vector quantities? For eg., Pressure( a scalar) equals force (a vector) divided by area (a vector).
What is the XY problem? What is the XY problem?  When asking questions, how do I recognize when I'm falling into it?  How do I avoid it? What noun or adjective would one give to a person that is intolerant of stupidity? A person that becomes annoyed, angry, or of very short temper when conversing or interacting with people of a lower intelligence?  For example:       The man is very xyzxyz; his son can't do multiplication very well.     or     She is a(n) xyzxyz. She gets very frustrated when people forget things.   I'm looking almost for a scientific/medical/psychological term. One that would fall into the same kind of group as words like haemophiliac, masochist, nihilist, etc. Why are the solutions of polynomial equations so unconstrained over the quaternions? An $n$th-degree polynomial has at most $n$ distinct zeroes in the complex numbers.  But it may have an uncountable set of zeroes in the quaternions.  For example, $x^2+1$ has two zeroes in $\mathbb C$, but in $\mathbb H$, ${\bf i}\cos x + {\bf j}\sin x$ is a distinct zero of this polynomial for every $x$ in $[0, 2\pi)$, and obviously there are many other zeroes.  What is it about $\mathbb H$ that makes its behavior in this regard to be so different from the behavior of $\mathbb R$ and $\mathbb C$?  Is it simply because $\mathbb H$ is four-dimensional rather than two-dimensional? Are there any theorems that say when a ring will behave like $\mathbb H$ and when it will behave like $\mathbb C$?   Do all polynomials behave like this in $\mathbb H$? Or is this one unusual? I am trying to perform centrality analysis with sDNA with ArcGIS Pro (ver. 2.7.1). However, I have failed to run the Preparation &amp; Integral Analysis in sDNA with the same reason. What is the problem and What should I do? Trying to purge MySQL fails I'm running in circles currently, trying to fix some mysql problem.  I couldn't use apt-get for a while now, because it always stuck at the line Setting up mysql-server-5.6 (5.6.27-0ubuntu0.15.04.1) ... and didn't let me do anything. So I tried to reinstall mysql, purging it. While I was able to remove mysql-server and mysql-client eventually, I'm still unable to purge mysql-common. Obviously, I managed to corrupt something, but how can I get my system back and running at this point?  ...:~# apt-get purge mysql-common Reading package lists... Done Building dependency tree        Reading state information... Done The following packages will be REMOVED:   mysql-common* 0 upgraded, 0 newly installed, 1 to remove and 5 not upgraded. After this operation, 0 B of additional disk space will be used. Do you want to continue? [Y/n] Y (Reading database ... 423600 files and directories currently installed.) Removing mysql-common (5.6.27-0ubuntu0.15.04.1) ... Purging configuration files for mysql-common (5.6.27-0ubuntu0.15.04.1) ... update-alternatives: error: /var/lib/dpkg/alternatives/my.cnf corrupt: invalid status dpkg: error processing package mysql-common (--purge):  subprocess installed post-removal script returned error exit status 2 Errors were encountered while processing:  mysql-common E: Sub-process /usr/bin/dpkg returned an error code (1)   -  ...# sudo dpkg -P --force-all mysql-common (Reading database ... 424733 files and directories currently installed.) Removing mysql-common (5.6.27-0ubuntu0.15.04.1) ... Purging configuration files for mysql-common (5.6.27-0ubuntu0.15.04.1) ... update-alternatives: error: no alternatives for my.cnf dpkg: error processing package mysql-common (--purge):  subprocess installed post-removal script returned error exit status 2 Errors were encountered while processing:  mysql-common   -  ...:~# lsb_release -a No LSB modules are available. Distributor ID: Ubuntu Description:    Ubuntu 15.04 Release:    15.04 Codename:   vivid   My goal is to just get it back and running again (mysql). prove that : $ i = \sqrt {-1}\ $ i have a pretty nasty question. i was glancing through a few olympiad papers and stumbled upon this question:  prove that  $ i = \sqrt {-1}\ $.  i tried the conventional methods namely euler's formula  but could not figure what to do next. how do you actually proceed further? i have checked a few books and a proof is not available.are there any proof available for this Over at , there is overlapping text in the Database Schema under Close-As-Off-Topic-Reason-Types:  that makes it really hard to read.  This is also happening underneath &quot;Pending Flags&quot;, and seemingly with every long line in the schema.  This would be fine if you could increase the width of the list as you can with the height, which would in theory separate the lines, but you can't.  Can we fix this, please?  UPDATE: I have found that  post is almost exactly the same as mine, but steady on with duplicate votes.   comment says that it will be fixed, but that question was asked more than five years ago, and in that time the problem has not been resolved.  UPDATE 2: It seems that  would help.  I changed a little CSS/HTML, and came up with this:  Although mine is a little cruder than it could be.  This is just an example. Prove that $\phi(n) \geq \sqrt{n}/2$ So I'm trying to prove the following two inequalities: $$\frac{\sqrt{n}}{2} \leq \phi(n) \leq n.$$ The upper bound we get from simply noting that $\phi(n) = n \prod_{p | n}\left( 1 - \frac{1}{p}\right)$ and the fact that $(1 - \frac{1}{p}) \leq 1$. But how can we get the lower bound? I tried using the same expression for $\phi(n)$ but it seems to not really give me the inequality. Can you help? Finding solutions to congruence equations Simplest or nicest proof that $1+x \le e^x$ The elementary but very useful inequality that $1+x \le e^x$ for all real $x$ has a number of different proofs, some of which can be found online. But is there a particularly slick, intuitive or canonical proof? I would ideally like a proof which fits into a few lines, is accessible to students with limited calculus experience, and does not involve too much analysis of different cases. Evaluation of Differentiation and Integration I was having some thought about what would be the syntax to make the end point evaluation of derivatives or integrals. Such as making the | with the two end points of evaluation on the top an bottom of the line. Any suggestions would be wonderful. Is there a proof of existence of time? It seems to me that there is no such thing as time. There  is only movement in the universe and we compare our own movement to a different object to have a sense of time. It can be a clock or a atomic vibration.  Does this view of time work within the current framework of phsics?  Do physicists have an explanation/proof about time's existence? In JUnit 3, I could get the name of the currently running test like this:  public class MyTest extends TestCase {     public void testSomething()     {         System.out.println("Current test is " + getName());         ...     } }   which would print "Current test is testSomething".   Is there any out-of-the-box or simple way to do this in JUnit 4?  Background: Obviously, I don't want to just print the name of the test. I want to load test-specific data that is stored in a resource with the same name as the test. You know,  and all that. I can't update 12.04 LTS. The Update Manager shows this:  CD/DVD 'Ubuntu 12.04 LTS _Precise Pangolin_ - Release i386 (20120423)' is required Please insert the above CD/DVD into the drive '/media/cdrom/' to install software packages from it.   The image I downloaded and burned to CD is from  the PC (Intel x86) desktop CD version. I burned many CDs but the result is the same. Prove that if W is a subspace of a finite dimensional vector space V, then dim(W) ≤ dim(V). My attempt at a solution:  Proof  Given a vector space $V$, let $S={v_1,...,v_n}$ be a basis for $V$. Consequently $\dim(V)=n$. Now given $W$, a subspace of $V$, it will be shown that $\dim(W)\le \dim V$   First, consider the case where $W=${0}. Then $dim(W)=0 \le\ n$,   Subsequently, consider the case for $W=V$. Then it follows that $dim(W)=dim(V)=n$.  Finally, consider the case where $W \subset V$ and without loss of generality assume $v_n \notin W$. Let $T={v_1,...,v_k}$ where $k\lt n$ be a basis for the subspace W. Now, since S is a basis for V, for every $v_i \in S$,  $c_1v_1+...+c_nv_n=0$ has only the trivial solution, thus none of the vectors in S can be expressed as linear combinations of the other vectors in S. It follows that the set T is not a basis for V as $v_n$ cannot be generated from T. The $dim(W)$ is given by the number of vectors in the basis. Therefore, $dim(W)=k \lt n$  Therefore, it has been shown that if $W \subseteq V$ then $dim(W) \le dim(V)$ Is acceleration relative in relativity? Suppose a box A is moving relative to a Box B, then by time dilation equation if I take 1 sec passed for an observer in A then for an observer in B will be little longer. Now if I suppose that the box B is moving while A is stationary under the same condition, then by the time dilation equation time passed in B must be shorter than A. How is this issue resolved? In the twin paradox problem my book says that it's due to acceleration, but in my opinion acceleration is relative (please correct me if I'm wrong), but here it is not the case. I have this problem: I'm used to compile and run .c files with CodeBlocks. If I do that from my Desktop (ext4 partition) it works without problems, but doing this from my secondary hard drive (NTFS partition) makes CodeBlocks to say permission denied while running a .c file.  I have read it's because of the partition type is it correct? But I don't know how to solve it. I tried to edit fstab (sudo gedit /etc/fstab) adding this line:   /dev/sda /media/Dati ntfs user,exec 0 1   but after rebooting Ubuntu I had a warning on boot about a problem mounting a drive, that's because I set KDE to auto mount my Dati drive on boot.   So I should auto mount my NTFS drive with execute permission? How can I do that? Is there a catch-all place on the Stack Exchange network where one can post any question that does not obviously belong to the Stack Exchange sites? Is there a catch-all place somewhere on the Stack Exchange sites where one can post a (any) question that does not obviously belong to any of the Stack Exchange sites?  Sometimes I have questions but I don't want to ask them on other sites (no need for names). I prefer to post it on the Stack Exchange network for various reasons.  If there isn't, are there plans for one? I imagine that if such a site exists, questions on that site can also be moved to other more specific sites when they exists, and it's not to be used to post questions which obviously belong to a specific Stack Exchange site. Add a rule after chapter title using titlesec Does Windows still rely on MS-DOS? I am just about to start an OS course and as an Apple user I am not very familiar with the underlying details of Windows OS. I was wondering, is MS DOS still used with Windows running on top or is ONLY Windows used now as the OS? I was a little confused because I read somewhere that MS-DOS is used for booting but Windows has all other OS capabilities built into it and thus is used for all other OS operations...