How was Molly Weasley powerful enough to Kill Bellatrix Lestrange?
How was this character killed without Avada Kedavra?
How to prevent unification when animating in photoshop? I am trying to create an animated gif where text drops down and smashes into the background and cracks it. Whenever I try and transform it though, the transformation is applied to all frames. How do I prevent this? I'm using Adobe Photoshop CS6 (64-bit) How to capture ordered STDOUT/STDERR and add timestamp/prefixes? Finding acute triangle probability A stick is broken in three parts of any length ,  if we join the pieces then what's the probability of getting a acute angled triangle? beamer - global transition shifts slide content Using beamer with the , I want to have a global transition effect (a fast fade) which I set using the following code:  \addtobeamertemplate{background canvas}{\transfade[duration=0.2]}{}   as found on  answer.  However, doing it messes up with my slides settings. It doesn't change every slides, only the \section ones that are slightly shifted to the right, adding a white line on the left, as seen here:   I tried using XeLaTeX and LuaLaTeX, as they are the only compilers I could use for my current font, but they both have the same issue.  It probably comes from the theme, however I have no clue why it would happen or how to fix it.  Edit :   \documentclass{beamer} \usetheme{m} \addtobeamertemplate{background canvas}{\transfade}{}  \begin{document} \section{test} \end{document}   Requires the mtheme to work Objective-C Blocks and variable scope Here's the problem: if $S = \mathbb{Q}[x]/(x^2)$, compute the group  of automorphisms $\mbox{Aut}(S)$.   First off, I have the solution and I know it's isomorphic to the multiplicative group $\mathbb{Q}\backslash\{0\}$, so I'm trying to understand it. It uses what is called the substitution principle and the fact that the restriction of any endomorphism $\phi: \mathbb{Q}[x]\to \mathbb{Q}[x]$ to $\mathbb{Q}$ is the identity. It says that these two facts implies that the endomorphisms of $\mathbb{Q}[x]$ are in 1-1 correspondence with $h \in \mathbb{Q}[x]$, where the endomorphism corresponding to $h$ is $\phi_h : \mathbb{Q}[x] \to \mathbb{Q}[x]$ given by $\phi_h(f) = f(h)$ for $f \in \mathbb{Q}[x]$. I guess I just don't understand how it applied the substitution principle? It's probably obvious, but for some reason I am not getting it.  An explanation would be greatly appreciated! Or if you have a different solution, that'd be cool too. Thanks!! Is it possible to overload the null-coalescing operator for a class in C#?    Say for example I want to return a default value if an instance is null and return the instance if it's not. The code would look like something like this:     return instance ?? new MyClass("Default");     But what if I would like to use the null-coalescing operator to also check if the MyClass.MyValue is set? Merge two arrays as key value pairs in PHP I've got two arrays of the same size.  I'd like to merge the two so the values of one are the key indexes of the new array, and the values of the new array are the values of the other.  Right now I'm just looping through the arrays and creating the new array manually, but I have a feeling there is a much more elegant way to go about this.  I don't see any array functions for this purpose, but maybe I missed something?  Is there a simple way to this along these lines?  $mapped_array = mapkeys($array_with_keys, $array_with_values); I've been programming in Java for a while and just got thrown onto a project that's written entirely in C#.  I'm trying to come up to speed in C#, and noticed enums used in several places in my new project, but at first glance, C#'s enums seem to be more simplistic than the Java 1.5+ implementation.  Can anyone enumerate the differences between C# and Java enums, and how to overcome the differences?  (I don't want to start a language flame war, I just want to know how to do some things in C# that I used to do in Java).  For example, could someone post a C# counterpart to Sun's famous Planet enum example?  public enum Planet {   MERCURY (3.303e+23, 2.4397e6),   VENUS   (4.869e+24, 6.0518e6),   EARTH   (5.976e+24, 6.37814e6),   MARS    (6.421e+23, 3.3972e6),   JUPITER (1.9e+27,   7.1492e7),   SATURN  (5.688e+26, 6.0268e7),   URANUS  (8.686e+25, 2.5559e7),   NEPTUNE (1.024e+26, 2.4746e7),   PLUTO   (1.27e+22,  1.137e6);    private final double mass;   // in kilograms   private final double radius; // in meters   Planet(double mass, double radius) {       this.mass = mass;       this.radius = radius;   }   public double mass()   { return mass; }   public double radius() { return radius; }    // universal gravitational constant  (m3 kg-1 s-2)   public static final double G = 6.67300E-11;    public double surfaceGravity() {       return G * mass / (radius * radius);   }   public double surfaceWeight(double otherMass) {       return otherMass * surfaceGravity();   } }  // Example usage (slight modification of Sun's example): public static void main(String[] args) {     Planet pEarth = Planet.EARTH;     double earthRadius = pEarth.radius(); // Just threw it in to show usage      // Argument passed in is earth Weight.  Calculate weight on each planet:     double earthWeight = Double.parseDouble(args[0]);     double mass = earthWeight/pEarth.surfaceGravity();     for (Planet p : Planet.values())        System.out.printf("Your weight on %s is %f%n",                          p, p.surfaceWeight(mass)); }  // Example output: $ java Planet 175 Your weight on MERCURY is 66.107583 Your weight on VENUS is 158.374842 [etc ...] When should a verb be followed by a gerund instead of an infinitive? How to show that the nth power of a $n \times n$ nilpotent matrix equals to zero $A^n=0$ $A$ is a $n\times n$ matrix such that $ A^m = 0 $ for some positive integer $m$.   Show that $A^n = 0$.   My attempt: For $n &gt; m$, it's obvious since matrix multiplication is associative.  For $n &lt; m$, $A^n\times A^{m-n} = 0$; not sure what to do next. Also I know that $\det A = 0$. In Iron Man 3,      When the real villain kidnapped the President of the United States,   it is never explained why none of the other Avengers came to help, or why Tony didn't call them. The only explanation so far is: "it was an Iron Man movie...", but an in universe answer would be good. Family in GLM - how to choose the right one? When modeling data sampled in the field, I often come across the problem of determining the Family of the dependent variable for GLM (or GLMM). An example: in an ecological study, I have ~ 60 patches.  I have sampled territories of an animal species within these patches as well as a set of explanatory variables.  The number of territories per patch (NTP) is the dependent variable in a GLM.   NTP is integer with values between 0 and 14:      How can I test for the family of NTP?  Any help appreciated as this is an issue many ecologists come across each time they conduct statistical analysis. Why are Bitmap-Fonts used automatically? How do I call a .NET assembly from C/C++? Suppose I am writing an application in C++ and C#.  I want to write the low level parts in C++ and write the high level logic in C#.  How can I load a .NET assembly from my C++ program and start calling methods and accessing the properties of my C# classes? $2+2 = 5$? error in proof $$\begin{align} 2+2 &amp;= 4 - \frac92 +\frac92\\ &amp;= \sqrt{\left(4-\frac92\right)^2} +\frac92\\ &amp;= \sqrt{16 -2\times4\times\frac92 +\left(\frac92\right)^2} + \frac92\\ &amp;= \sqrt{16 -36 + \left(\frac92\right)^2} +\frac92\\ &amp;= \sqrt {-20 +\left(\frac92\right)^2} + \frac92\\ &amp;= \sqrt{25-45 +\left(\frac92\right)^2} +\frac92\\ &amp;= \sqrt {5^2 -2\times5\times\frac92 + \left(\frac92\right) ^2} + \frac92\\ &amp;= \sqrt {\left(5-\frac92\right)^2} +\frac92\\ &amp;= 5 + \frac92 - \frac92 \\ &amp;= 5\end{align}$$  Where did I go wrong I want to subscribe to the newsletter on my work email address but still have everything else go to my normal SO email account. I don't have a way to set up a forwarding filter from my normal email account.  Any way I can do this? Can I recover app data after the phone has been Factory Reset? When I slam my hand onto my keyboard, only a maximum of 6 keys will be registered, I've tested this for the past few minutes and was unable to get more than 6. Is this the same on all keyboards? If not, what would be the distinguishing factor, If yes: why 6 specifically?  For clarification: I do not have a usecase for this, I am simply curious So I understand the concept of gravity, in that it's not actually a force, but more of a displacement in the spacetime grid. An object with a big enough mass will bend the spacetime, causing smaller objects to "attract" to it (not really, but good enough for what I am trying to figure out)   Ok so that makes sense, but what I am not understanding is, how come planets don't just get engulfed by the Sun? There must be something acting against the gravity for the planet to be a certain distance away from the sun. Am I not understanding this concept correctly?