Triangle law of vector addition for parallel vectors
Laws of addition of Vectors
How can I identify an anonymous inner class in a NotSerializableException How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number? How many digits does $2^{1000}$ contain? I tried this way, I only need to know if this is correct or if there are better ways to solve this:  $2^{1000}$ does not have a factor of $5$ obviously therefore we can assume  $$ 10^{m} &lt; 2^{1000} &lt; 10^{m+1}$$ for some  $m$   Assume $ k = 2^{1000}$, then take log on both sides $\log k = 1000  \log 2 \approx 301.02999 &gt; 301$  Therefore $2^{1000}$ has $302$ digits. I am trying to automate these steps so that I don't need to do this on every machines manually. I need to install latest app server software (abc.tar.gz) on all the unix boxes.  I need to do this in around 12 machines - "machine1" ... "machine12". I have a master machine "machine0" which has abc.tar.gz file so I was thinking to run my script from this machine only and install abc.tar.gz software by following below steps in all those 12 machines one by one. My unix account id is david and my process runs as golden user.  This is the steps I follow if I am installing abc.tar.gz in "machine1":  david@machine1:~$ sudo scp david@machine0:/home/david/abc.tar.gz . david@machine1:~$ sudo stop test_server david@machine1:~$ sudo su - golden golden@machine1:~$ cd /opt/process golden@machine1:/opt/process$ rm -rf * golden@machine1:/opt/process$ exit david@machine1:~$ sudo cp abc.tar.gz /opt/process david@machine1:~$ sudo chown -R golden /opt/process david@machine1:~$ sudo su - golden golden@machine1:~$ cd /opt/process golden@machine1:/opt/process$ tar -xvzf abc.tar.gz golden@machine1:/opt/process$ exit david@machine1:~$ sudo start test_server   How can I automate this so that it can do the same steps in all 12 machines one bye one? I mean install abc.tar.gz in machine1 first, then install on machine2 and go on..  I want to run this script from machine0 only.  Is there any way to automate this? Prove that $\left(\sum^n_{k=1}x_k\right)\left(\sum^n_{k=1}y_k\right)\geq n^2$ If $x_1,...,x_n$ are positive real numbers and if $y_k=1/x_k$, prove that $$\left(\sum^n_{k=1}x_k\right)\left(\sum^n_{k=1}y_k\right)\geq n^2.$$   I've been learning induction, and I've come across this problem that I really can't even break down and begin to think about. I've been told it has something to do with Cauchy-Schwarz, but I cannot figure out how to apply it. I would appreciate help figuring out how to go about and formulate this proof. Thanks! How to add CC to a webform email? I'm using Drupal 7.  Is it possible to add a CC to a webform email?  I was using   function theme_webform_mail_headers($variables) {   $headers = array(     'X-Mailer' =&gt; 'Drupal Webform (PHP/' . phpversion() . ')',   );   return $headers; }   changing it with      function MYTHEME_webform_mail_headers($variables) {       $headers = array( 'CC' =&gt; 'ccmeail@domain.com', 'X-Mailer' =&gt; 'Drupal Webform (PHP/'. phpversion() .')',  );       return $headers;     }   It does not work, I've cleared all the chaches and it does not add the CC. How could I add the CC?  Thanks in advance. Find all integer solutions to $x^2+4=y^3$. What do you call a person who "shuts down" ideas? Stack Overflow reputation in CV Should I mention my Stack Overflow (and other Stack Exchange sites) reputation in my CV while applying for a post-graduate position? There is a type and search drodown which will appear after user type in the value. I need to click on the dropdown which contains the name of the drop down field.   The problem here is that there is no unique attribute present (No unique class, no unique name) &amp; the id keeps on changing after every login so cannot take id also. I need to get the size of directory in terminal for signing purposes. I'm using following command:  du -s /path/to/dir   I'm multiplying the result by traditional UNIX block size (512 bytes) and get actual directory size in bytes. However, the Finder's "Get Info" dialog window shows the size slightly smaller than the one calculated with the terminal command. And it seems that it's reproducible on any folder/bundle. What am I missing? How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$ How to prove $x^a-1\mid x^b-1 \iff a \mid b$, where $x \ge 2$ and $a,b,x \in \Bbb Z$.  I've tried the following in attempting to solve this:  $$a\mid b \Rightarrow aq=b \Rightarrow x^{aq}=x^b \Rightarrow x^ax^q=x^b$$  Because $x^q \in \Bbb Z$, it follows that $x^a\mid x^b$.  This is as far as I have gotten; any help getting further is appreciated.  Note: It may be that this identity is not true at all? Let $Z_n$ be the set of all $n \times n$ matrices that commute with all $n \times n $ matrices. Show that $$Z_n = \{\lambda I_n \ | \  \lambda \in \mathbb R\}$$  ($I_n$ is the $n \times n$ identity matrix)  I don't know how to use $E_{ij}$ (matrix with $1$ in $(i,j)$ and $0$ elsewhere) and the elementary matrix $P_{ij}$ to prove this question. Can anyone explain it please? Custom right-click action in Unity Launcher keeps cursor busy for 20 seconds To have a "minimize window" option through right click on an icon in the Unity launcher (Ubuntu 14.04), I followed the detailed instructions  about changing a .desktop file and made a custom Firefox launcher in ~/.local/share/applications/ folder. The relevant part of the .desktop file is:  Actions=NewWindow;NewPrivateWindow;Minimize  [Desktop Action NewWindow] Name=Open a New Window Exec=firefox -new-window OnlyShowIn=Unity;  [Desktop Action NewPrivateWindow] Name=Open a New Private Window Exec=firefox -private-window OnlyShowIn=Unity;  [Desktop Action Minimize] Name=Minimize Windows Exec=sh /home/myusername/Documents/xdotool_sh/minimize.sh firefox OnlyShowIn=Unity;   The desktop action "Minimize" invokes a simple shell script, minimize.sh that has the following content:  #/bin/bash name=$1 for i in $(xdotool search --class "$name"); do     xdotool windowminimize $i done   The script uses xdotool, that can be installed from the official repositories, to find all the firefox windows, iterate over them and minimize them.  The script works and the launcher right menu option "Minimize Windows" works as well, but as soon as the windows are minimized, the mouse pointer gets in "busy" mode and stays like this for about 20 seconds (although the mouse actions are still responsive).   Does anyone know why starting a shell script from a right menu option in Unity could lead to this behaviour?  EDIT: Apparently the wait period is inevitable, as explained in Jacob Vlijm's answer. Since the mouse remains responsive, avoiding the transformation of the pointer in the spinning wheel is a partial esthetic workaround, as explained on .  EDIT2: giving the system a fake window is a better solution, as explained by Jacob below. Which repository source do I need to add to my sources.list to access the package firmware-linux-nonfree?  I am using Deb 6 testing 32 bit. How can I remap Caps lock to both Escape and Control? I generally run Linux. I use Vim a lot, so the Escape key is extremely important. I also use other keyboard shortcuts a lot, so Control is "key" as well. On Linux, I've solved this by using  to map the Caps lock key to Escape if pressed by itself, or Control if pressed in combination with another key. This puts the best of both worlds within quick reach of my pinky finger. Is there any way I can do this on a Mac? Combine the output of two commands in bash Is it possible to combine output from these two commands?  node ~/projects/trunk/index.js  python ~/projects/trunk/run.py run   Neither command exits so I'm not sure how to do this. How can we recover the Newtonian gravitational potential from the metric of general relativity? Current Configuration: I have two SQL Servers, which are connected by the failover mechanism, meaning one is primary and one is secondary. I restarted both services on both servers sequentially. On the secondary server, all the databases are in the &quot;Synchronizing&quot; state. AG replication mode is synchronous. It has been 12hr it's still showing &quot;Synchronizing&quot; state. What I did so far to resolve Drop the database from the secondary server and remove the database from AG group on the primary server and add it back. Any insight on this, I am using SQL Server 2017. I am looking for a multivariable calculus book that is really physics oriented.  Anyone know of any?  EDIT: My wife is looking to brush up on multivariable at the same time she needs to brush up on the related physics.