how to unlock bluetooth service in Ubuntu 15.10
How do you make Ubuntu accept files sent over bluetooth
Where M is a matrix calculate a formula for M^n Let $$M = \begin{bmatrix} -7 &amp; 8 \\ -8 &amp; -7 \end{bmatrix}.$$ Find formulas for the entries of $M^n$ where $n$ is a positive integer.  (Your formulas should not contain complex numbers.)  Your answer should be in the form of a matrix.  I diagonalized to the form $M = P D P^{-1}$  and $M^n = P D^n P^{-1}$ where $P$ is my matrix of eigenvectors and $D$ is my matrix of eigenvalues.  My final answer after diagonalization was $$M^n = \begin{bmatrix} .5((-7+8i)^n+(-7-8i)^n) &amp; (i/2)(-(-7+8i)^n+(-7-8i)^n) \\ (.5/i)(-(-7+8i)^n+(-7-8i)^n) &amp; .5((-7+8i)^n+(-7-8i)^n) \end{bmatrix}$$  I can't seem to find an answer not in terms of complex numbers.  Can someone show me what I'm missing? Selecting a security team that includes at most one of the oldest man or oldest woman A security company consists of $7$ men and $6$ women. Determine the number of ways to form the night shift team of $3$ men and $3$ women if it can include at most one of the oldest man or oldest woman.  I know the first step is to pick $3$ from each group which is   $_6C_3 \cdot _7C_3 $  but I am not sure how to account for the "include at most one of the oldest man or oldest woman"   The answer is $_6C_3 \cdot _7C_3 + _6C_3 \cdot _5C_3 + _6C_2 \cdot _5C_3 $  Also, how do I account for it in my calculations if I want to include the oldest man and oldest woman from the group? Cycles: How do I exclude the Environment Texture from reflections? In a Cycles scene I have an equirectangular image serving as an Environment Texture background (set in the World settings).  I have a glossy object being partially lit by the Environment Texture, as well as getting reflections from it.  Is there a way I can exclude the Environment Texture from affecting the glossy object completely? I want the image as background wallpaper only. The glossy object should be affected by other objects and lights within the scene: everything except the Environment Texture. I am trying to master the homemade Neapolitan pizza, from dough preparation to cooking it.  After following the recommendations at Seriouseats.com for the dough preparation, I came across some doubts regarding the oven use.  I understand that ideally I would make it in a 900F wood oven, but at home we don't have such equipment!  What is the best practice to make the Neapolitan Pizza in a regular gas oven that heats up to 530F? (i.e. temperature, time, tray positioning...) Are there changes in the way the dough has to be prepared? Add notes under the table I'm using the latex package  because the  package isn't using APA style version 6 yet.  Now I'm trying to add a table with notes right underneath it, like in this table for instance:    Since the \caption{} is used as a title above the table, I have to add an extra row for the notes that goes over the whole table width. The problem is that the notes won't fit into one line so I need multi-line cell. How can I accomplish that? Or am I doing it totally wrong and there is a much easier way? I guess footnotes don't work here.  \documentclass{apa6e}  \begin{document} \shorttitle{} \begin{table} \caption{title} \begin{tabular}{cc} foo &amp; bar\\ \hline \multicolumn{2}{l}{Notes. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Cras lacus orci, porttitor et posuere sit amet, tempor non justo. Ut quis aliquet turpis. Ut dictum nulla eget purus elementum a lacinia libero varius. Donec malesuada nulla ut odio rhoncus convallis. Aenean faucibus sollicitudin sapien, a vestibulum ante rhoncus sit amet. In vitae mi justo. In arcu metus, porta et lacinia ut, ultricies sed eros.} \end{tabular}  \end{table} \end{document} Let $\{a_n\}$ be defined as follows: $$a_1 = 2, a_{n+1}=\dfrac{1}{3-a_n}$$ $n \geq 1$.   Does $\{a_n\}$  converge?    Using the monotone convergence thereom, if the sequence is both bounded below and decreasing, $\forall n\in\mathbb{N}, n\geq 1$, then we can say the sequence converges.  I'm having trouble proving that the sequence is bounded below by induction.    Claim: The sequence is bounded below by $0$.  Base Case:  $n=1$  $a_1 = 2 \geq 0$, so this holds.  Induction Step  Suppose that $a_k \geq 0$, for some $k \in\mathbb{N}$. (IH)  Prove $a_k \geq 0\to a_{k+1} \geq 0$  I have some difficulty here.  $a_{k}=\dfrac{1}{3-a_{k-1}} \geq 0$  $a_{k+1}=\dfrac{1}{3-a_{k}}$, but we know $a_k \geq 0$, but we don't know how much bigger. It could be that $a_k = 4$, and then I have $a_{k+1}=\dfrac{1}{3-4}$, which is negative, and does not confirm with my claim of being bounded below by $0$. Have I gone somewhere wrong in my induction? How to run scripts without typing the full path? When do you use the "this" keyword? I was curious about how other people use the this keyword. I tend to use it in constructors, but I may also use it throughout the class in other methods. Some examples:  In a constructor:  public Light(Vector v) {     this.dir = new Vector(v); }   Elsewhere  public void SomeMethod() {     Vector vec = new Vector();     double d = (vec * vec) - (this.radius * this.radius); } What is the significance of the name Bleach? The name "Bleach" seems to be having no relevance to the plot unlike most other series. Was it just chosen at Kubo-sensei's whim or does it have some significance? Maybe some cultural significance associated with shinigami, etc. that I am now aware of? Hey all I downloaded this file () but can't seem to be able to uninstall it. I tried looking online as well as the README file but there is only instruction for installing, not uninstalling the package.   Attempted solutions:  sudo apt-get remove laptop_mode   returned   E: Unable to locate package laptop_mode   but when I type in laptop_mode I do get   Unhandled kernel version: 3.13 ('uname -r' = '3.13.0-32-generic')   Is there any way I can uninstall laptop-mode-tools? Are there other schools for witches and wizards in the rest of the world? In the books they only speak of 3 schools, but what about Asian or American people?  And even more, were they affected by the events happening in Europe? How do I find out which version and derivative of Ubuntu is right for my hardware in terms of minimal system requirements? Motivated by , can one prove that the order of an element in a finite group divides the order of the group without using Lagrange's theorem? (Or, equivalently, that the order of the group is an exponent for every element in the group?)  The simplest proof I can think of uses the coset proof of Lagrange's theorem in disguise and goes like this: take $a \in G$ and consider the map $f\colon G \to G$ given by $f(x)=ax$. Consider now the orbits of $f$, that is, the sets $\mathcal{O}(x)=\{ x, f(x), f(f(x)), \dots \}$. Now all orbits have the same number of elements and $|\mathcal{O}(e)| = o(a)$. Hence $o(a)$ divides $|G|$.  This proof has perhaps some pedagogical value in introductory courses because it can be generalized in a natural way to non-cyclic subgroups by introducing cosets, leading to the canonical proof of Lagrange's theorem.   Has anyone seen a different approach to this result that avoids using Lagrange's theorem? Or is Lagrange's theorem really the most basic result in finite group theory? How come such different methods result in the same number, $e$? I guess the proof of the identity $$ \sum_{n = 0}^{\infty} \frac{1}{n!} \equiv \lim_{x \to \infty} \left(1 + \frac{1}{x}\right)^x $$ explains the connection between such different calculations. How is it done? With the following AppleScript code within a "Run AppleScript" action in a Service:  tell application "System Events"     set theSBounds to {{572, 64}, {332, 515}}     set position of window "Google Hangouts - myemailaddress@gmail.com" of application process "Google Chrome" to item 1 of theSBounds     set size of window "Google Hangouts - myemailaddress@gmail.com" of application process "Google Chrome" to item 2 of theSBounds end tell   the Service will only work if the application from which that Service has been called has been added to the list of applications under "Allow the apps below to control your computer." This list is found at System Preferences → Security &amp; Privacy → Accessibility.  Is it possible to modify the AppleScript code somehow so that adding every application on one's computer to the list is not necessary? Or, so that, one only needs to add one item to the list, as opposed to every application on one's computer?  I thought that something like this might work:  do shell script "osascript -e 'tell application \"System Events\"' -e 'set theSBounds to {{572, 64}, {332, 515}}' -e 'set position of window \"Google Hangouts - myemailaddress@gmail.com\" of application process \"Google Chrome\" to item 1 of theSBounds' -e 'set size of window \"Google Hangouts - myemailaddress@gmail.com\" of application process \"Google Chrome\" to item 2 of theSBounds' -e 'end tell'" with administrator privileges   but this code also requires that the application from which the Service is run is added to the Accessibility list.  Note: I only want to run this AppleScript as a Service, and not in an Automator-created Application, because the code receives selected text as its input (system-wide). Interpretation of mean absolute scaled error (MASE) Use ALT to move windows in Windows like in Linux In most Linux window managers, one can use the Alt key while clicking and dragging to rearrange windows. This is one of my favorite features of Linux window managers.  Is there a way to do this in Windows 7? Installing from source - do I need to keep the extracted tarball directory If I'm installing from source, do I need to keep the extracted tarball directory?  So if I download the git tarball. I then do:  tar -xvzf git.tar.gz   This will create a git.x.x. directory, into which I cd, then run ./configure etc. Once I'm done with this process, and git, or whatever is installed, do I need to keep the original git.x.x extracted directory, or is that just used for compiling the program?  I'm somewhat confused by all the directories, and folders used for programs. Prove by induction that $$(a_{1}+a_{2}+\cdots+a_{n})\left(\frac{1}{a_{1}}+\frac{1}{a_{2}}+\cdots+\frac{1}{a_{n}}\right)\geq n^{2}$$  where $n$ is a positive integer and $a_1, a_2,\dots, a_n$ are real positive numbers   Hence, show that  $$\csc^{2}\theta +\sec^{2}\theta +\cot^{2}\theta \geq 9\cos^{2}\theta$$  Please help me.  Thank you! What is "Go" in cribbage? I've played a fair bit of cribbage, but I've never heard of scoring one point for "Go" (as mentioned in this other question: ).  What is it, and what impact does it have on the game?