How do I stretch a html5 video to width:600 and height 200?
HTML 5 Video stretch
Area of a parallelogram, vertices $(-1,-1), (4,1), (5,3), (10,5)$. I need to find the area of a parallelogram with vertices $(-1,-1), (4,1), (5,3), (10,5)$.  If I denote $A=(-1,-1)$, $B=(4,1)$, $C=(5,3)$, $D=(10,5)$, then I see that $\overrightarrow{AB}=(5,2)=\overrightarrow{CD}$. Similarly $\overrightarrow{AC}=\overrightarrow{BD}$. So I see that these points indeed form a parallelogram.  It is assignment from linear algebra class. I wasn't sure if I had to like use a matrix or something. I'm not particularly fond of apps cluttering my $HOME directory with their own files or directories. It's rarely a problem, because most apps have the courtesy to hide their data by prefixing it with a dot or conforming to the ~/.config standard. But not snap.  Q1: Have I misunderstood this directory?  Is ~/snap really a directory which I'm supposed to enter and access on a daily basis on a par with ~/downloads, ~/pictures, ~/work, etc?  Q2: In any case: Can I move it e.g. ~/.snap?  I can't find anything like /etc/snap, /etc/default/snap, or ~/.config/snap to tweak things. I tried export SNAP_USER_DATA=$HOME/.snap but it didn't work. Supremum and Infimum Let $A$ be a nonempty set of real numbers which is bounded below. Let $-A$ be the set of all numbers $-x$, where $x \in A$. Prove that $\inf A = -\sup(-A)$.   We know that $-A$ is bounded above. Hence $\sup(-A)$ exists. So to proceed, one would show that $\inf A \leq -\sup(-A)$ and $\inf A \geq -\sup(-A)$? Or $-\inf A &gt; \sup(-A)$ and $-\inf A &lt; \sup(-A)$.  I get the sense that one can use the following fact as well: (i) Let $\alpha = \sup S$. If $\beta &lt; \alpha$ then $\beta$ is not an upper bound for $S$. How to get string with pattern from std::regex in VC++ 2010 Blacklight CFL Bulb Effect? I have been searching everywhere, and I can't find an answer so I'm coming here!  I'm trying to create a CFL Blacklight bulb. I've attached a couple images below of what I've tried to make. I'd love to have an effect like this:    Does anyone know how to recreate this? It seems like the color is affected by time as the bulb heats up, eventually being all white-ish. That would be fine, too, but I can't even seem to get the lighting effect of the pink glow around it and whatnot. I can post pictures of my node setup if you need it, though I think I made it necessarily complicated.  Thanks in advance!  UPDATE: This is what I have now:   I want to adjust the colors, but that isn't the issue now... The way I made this is a glass spiral that acts as the bulb. Inside of that bulb (that has a glass-like shader) is a purple material that I made that mimics the phosphor coating blacklight light bulbs have to filter light. Then, a separate mesh spiral is inside of that, and it has the emission stuff on it.   As Duarte suggested, I used the node setup he had for my emission, but used a transparent node instead of glossy. Why isn't the emission light from inside my glass causing the glass to be glossy? If I put a point light in the scene, it looks glossy.   Thanks in advance! Is $0$ a natural number? Is there a consensus in the mathematical community, or some accepted authority, to determine whether zero should be classified as a natural number?  It seems as though formerly $0$ was considered in the set of natural numbers, but now it seems more common to see definitions saying that the natural numbers are precisely the positive integers. How do I get a Ralink RT3290 wireless card working? On , there are download options for only certain logos/icons. Shouldn't this include all the graduated sites logos/icons? I think it should. This question is asked in various forms here but the question boils down to:  I know shrinking a database is risky. In this case, I've removed so much data and I'll never use it again.   How can I shrink my database? What files do I shrink?  What should my considerations be while doing this?  Should I do anything after? What if it is a large database? Can I shrink it in smaller increments? Why doesn't my screen lock in XFCE? How do I add a new language? The aftermarket ROM I use seems to have the language list parred down to just a couple selections, probably to save space.  I would like to add a language back into the system. I can already set the locale using programs such as  so that applications with my language support start with the right locale code, however that doesn't add missing system languages. Having the system in another language would be nice, but the main thing is getting the dictionary files for the keyboard auto-complete. How does one go about adding the language support files for an input language to a system or ROM?  I can access other ROM's or the AOSP project to rip things out, but I don't know where to start. What files do I need and what modifications need to be made? Is there an easy way to do this with say a language-pack or is it hackery all the way?  My ROM is fully rooted and I have adb access if necessary. It's Android 2.3.7 () and I'm using the stock Android keyboard. The language I want is Turkish, although unless somebody has a download to point me to it's mostly the process I'm looking for here. In JavaScript, the "this" operator can refer to different things under different scenarios.   Typically in a method within a JavaScript "object", it refers to the current object.  But when used as a callback, it becomes a reference to the calling object.  I have found that this causes problems in code, because if you use a method within a JavaScript "object" as a callback function you can't tell whether "this" refers to the current "object" or whether "this" refers to the calling object.  Can someone clarify usage and best practices regarding how to get around this problem?     function TestObject() {             TestObject.prototype.firstMethod = function(){                       this.callback();                       YAHOO.util.Connect.asyncRequest(method, uri, callBack);              }              TestObject.prototype.callBack = function(o){               // do something with "this"               //when method is called directly, "this" resolves to the current object               //when invoked by the asyncRequest callback, "this" is not the current object               //what design patterns can make this consistent?               this.secondMethod();             }             TestObject.prototype.secondMethod = function() {              alert('test');             }         } Add a confirmation before moving comments to a chat Does copying a spell from a scroll into your spellbook consume the scroll? The text on page 32 of the Basic Rules that talks about copying spells does not explicitly state that the process consumes the scroll. Does it? If $f$ is continuous, nonnegative on $[a, b]$, show that $\int_{a}^{b} f(x) dx = 0$ iff $f(x) = 0$  "$\Rightarrow$" Assume by contradiction that $f(x) \neq 0$ for some $x_0 \in [a, b]$. Without loss of generality, assume that $f(x_0) &gt; 0$. Since $f$ is continuous, $\exists \delta &gt; 0$ such that $f(x) &gt; 0,  \forall x \in (x_0 - \delta, x_0 + \delta)$. Since $f$ is continuous on $[a, b]$, then it is Riemann integrable. Therefore $\int_{a}^{b} f(x) dx = \sup L(f, p)$ for some partition $p$. Now what I want to do is to show that the lower sum, $L(f, p) &gt; 0$, in that case its supremum is $&gt;0$, and that contradicts the condition that $\int_{a}^{b} f(x) dx = 0$. However, I don't know how to articulate it.  "$\Leftarrow$" If $f(x) = 0, \forall x \in [a, b]$, then $\int_{a}^{b} f(x) dx = \int_{a}^{b} 0 dx = 0$ So I'm making this summary of a course where I've only been getting information from one book. Sometimes I want to show what page from the book a statement is taken from but I can't figure out a clean way of doing it.  Basically I would like to have something (in function) similar to:  "Statement[Book p123]"  Do you have any suggestions? I always see pictures of the solar system where our sun is in the middle and the planets surround the sun. All these planets move on orbits on the same layer. Why? Run apt-get without sudo Show that if $p$ is prime then $\Bbb Z_p$ is a field Check my proof please.  Let $\Bbb Z_p:=\Bbb Z/p\Bbb Z$ be the quotient ring modulo $p$. I want to prove that if $p$ is prime then $\Bbb Z_p$ is a field.  Known facts about the quotient rings of the kind $\Bbb Z_n$ (I dont list all the characteristics of a ring, just some ones):   They are commutative rings with unity. $[0]=[n]$ is the identity of addition or zero. Then $[n]+[a]=[a]$ and $[n]\cdot[a]=[n]$ for all $[a]\in\Bbb Z_n$. $[1]$ is the multiplicative identity or unity. Then $[1]\cdot[a]=[a]$ for all $[a]\in\Bbb Z_n$. The addition is defined as $[a]+[b]=[a+b]$, and the multiplication is defined as $[a]\cdot[b]=[ab]$. $[a]=[b]$ means that exists $z\in\Bbb Z$ such that $a=b+nz$. $|\Bbb Z_p|=p$.   A ring $\Bbb Z_p$ dont have zero divisors, i.e. doesnt exist $[a],[b]\in\Bbb Z_p$ distinct of $[p]$ such that $[a]\cdot[b]=[p]$. Proof by contradiction: suppose that exists such $[a],[b]$ distinct of $[p]$ that are zero divisors. Then exist some $z_j\in\Bbb Z$ such that:  $$(a+pz_1)(b+pz_2)=pz_3\iff ab+pz_4=pz_3\iff ab=pz_5$$  but this is a contradiction with the assumption that $a,b\neq p$ and $p$ prime, so dont exist divisors of zero on any $\Bbb Z_p$.$\Box$  For any $[a]\in\Bbb Z_p$ distinct of $[p]$ exist $[b]$ such that $[a][b]=[1]$. Because $\Bbb Z_p$ dont have zero divisors and is finite for some $[a]\neq[p]$ we have that if $[b]\neq[c]$ then $[a][b]\neq[a][c]$. Proof by contradiction: if $[a][b]=[a][c]$ in the above conditions then  $$[a][c]=[ac]=[ab]=[a][b]\iff ac+pz_1=ab+pz_2\iff a(c-b)=pz_3$$  for some $z_j\in\Bbb Z$. But $pz_3\in[p]$, then $[a][c-b]=[p]$ but because there are no zero divisors in $\Bbb Z_p$ then or $[a]=[p]$ or $[c-b]=[p]$ what contradicts the above conditions.$\Box$  Because $[a][b]\neq[a][c]$ for $[a]\neq[p]$ and $[b]\neq[c]$ then for any $[a]\neq[p]$ we have that  $$[a]\cdot\Bbb Z_p=\Bbb Z_p\implies \exists [b]\in\Bbb Z_p:[a][b]=[1]$$  In other words: every element of $\Bbb Z_p$ but $[p]$ have a multiplicative inverse as stated above.$\Box$  Because $\Bbb Z_p$ is a commutative ring with $[1]\neq[0]$ and have multiplicative inverse for all their elements but $[p]=[0]$ then $\Bbb Z_p$ is a field.$\Box$ Pre-declare all private/local variables?