Are all undead evil?
What rules say that summoning undead is evil, and what rules say why?
Can a parallel computer simulate a quantum computer? Is BQP inside NP? Do opposite categories always exist? How do you change the size of figure drawn with Matplotlib? How to increase swap size? How to use SSH to run a local shell script on a remote machine? Solving $\textbf{r}''(t)=\frac{GM}{(r(t))^3}\textbf{r}(t)$ I have the following problem that I don't know how to solve:  Let $\textbf{r}(t)$ be a curve and let $r(t):= |\textbf{r}(t)|$. Let the curve $\textbf{r}(t)$ be defined by: $$\textbf{a}(t)=\frac{GM}{(r(t))^3}\textbf{r}(t)$$ Where $\textbf{a}(t) = \textbf{r}''(t)$ is the acceleration of the particle and $G,M \in \mathbb{R}$. Suppose that $\textbf{r}(t)$ and $\textbf{r}'(t)$ are not parallel. The objective is to determine the trajectory $\textbf{r}(t)$ in polar coordinates.  So basically we have the following equation: $$\textbf{r}''(t)=\frac{GM}{(r(t))^3}\textbf{r}(t)$$ The thing is that I don't know how I should proceed from now on. If we'd have just normal scalar function this would be a differential equation and I think I would be able to solve it, but like this I have no idea how to approach the problem. How can I solve this?  Edit: If $$\textbf{r}(t):=(x(t),y(t))$$ then the equation turns into the following system of equations: $$x''=\frac{GM}{(\sqrt{x^2 + y^2})^3}x$$ $$y''=\frac{GM}{(\sqrt{x^2 + y^2})^3}y$$ I don't know if this helps but I think that this turns thing easier perhaps. Chrome S3 Cloudfront: No 'Access-Control-Allow-Origin' header on initial XHR request Best way to store currency values in C++ How to show that $K\leq S_4$ is a normal subgroup? Let $K=\{(1),(1,2),(3,4),(2,4),(1,4),(2,3)\}$ is a subgrope of $S_4$, we want to show that it is a normal subgroup.  I know that i have to examine the condition of normality in $S_4$ i.e. for all $g\in S_4, g^{-1}Kg=K$. I think this takes times or I am missing something near. Please give me the right hint. Thank you.  Edit: $K = \{(1),(12)(34),(13)(24),(14)(23)\}.$ What are the pieces of evidence that universe is expanding? What makes a photo a good photo? I don't know if this is a stupid question, this just came across my mind.  Imagine a photo of a dog yawning.  Someone could say that is a very good photo as it is taken just at the right moment, from a perfect angle (eg. level with the dog) and it has a shallow depth of field focusing on its face.  Someone else might dislike it because unfortunately the dog is ugly.  So from that example I could say people look at the following elements when judging a photo (but I could be wrong):   The timing (if it's taken at the right moment) The angle it's taken from (composition?) DOF (composition?) The subject (eg. whether the dog is pretty)   I am interested to know what experts think the elements you look at when judging whether a photo is a good photo.  Thanks in advance for your comments. How to Uninstall Blender Software I installed Blender for a project working on and it's way more than I need. I'd like to uninstall it, but can't figure out how to do so. It's not showing up in Programs (using Windows 9) and I can't find instructions on how to remove it in the Blender documentation. Any assistance would be greatly appreciated. Thanks. Alternative to LibreOffice Base for Ubuntu Addition with NULL values No icons for automounted volumes on GNOME / Nautilius desktop on Ubuntu 19.04 Up to Ubuntu 18.04, using default GNOME/Nautilius desktop, when I inserted a (data file) USB stick it would automount and put a USB icon onto the desktop.  I find this very useful, especially for quick eject via context menu.  Now at 19.04, on USB insertion I do see a "banner" appear for a few seconds, but I no longer get any desktop icon .  I run under VirtualBox on Windows, but that has not changed and I do not think is at issue.  Ubuntu does still automount the stick at /media/&lt;username&gt;.  I found .  I checked in dconf-editor and both keys, including org.gnome.desktop.media-handling.automount-open, are set. The  spell says time stops for other creatures.  What all is affected by the spell? Is gravity affected? Air movement?  I know that the spell only does what it says, and nothing else, but just wondering.   In addition, is it saying that the other creatures are not affected by environmental effects and the like while time is stopped?  For instance, if a wind blew really hard at one of the creatures you're fighting, would it affect that foe while time stop is active? If you were to place a bear trap behind the person, and a hard wind blew enough to tip them, would they then fall over onto the bear trap and be damaged without the spell ending?  This is a very curious spell... I would like to transfer files between two remote hosts using on local shell, but it seems rsync doesn't support synchronisation if two remotes are specified as follow:  $ rsync -vuar host1:/var/www host2:/var/www The source and destination cannot both be remote.   What other workarounds/commands I could use to achieve similar results? Undergraduate prerequisites for a Ph.d. in combinatorics I am a double major in mathematics and electrical engineering. Towards the end of my mathematics major, I began to develop an interest in combinatorics (specifically graph theory), and am seriously considering a Ph.D. in the subject.   Having developed the interest late, my senior thesis will be in a different topic (complex ODEs), but I would have completed one course in combinatorics/graph theory (an upper-level undergraduate course using a grad-level text - I expect a strong reference from the professor teaching this course).   The courses I have completed are basically both the undergraduate and graduate-level algebra sequence,  analysis in R and R^n (without a formal introduction to Lebesgue measure), discrete math (for EECS), applied probability, one course in numerical methods, PDEs, applied complex variables, and a "mathematical methods for sciences" course (focusing on special functions, variational calculus, and integral transforms).   I won't have the standard math major courses(i.e,  topology, measure theory, and number theory.) I plan to focus more on applications than theory in my combinatorics Ph.D.   Would additional coursework be necessary for a Ph.D. in combinatorics (specifically graph theory)? (I could potentially delay my degree by a year and spend time as a non-degree student at another university, or complete a non-thesis track master's degree before applying for a masters/Ph.d.). Any advice would be appreciated. I am in the middle of a problem and having trouble integrating the following integral:  $$\int_{-1}^1\frac1{(1+x^2)^2}\mathrm dx$$  I tried doing partial fractions and got:  $$1=A(1+x^2)+B(1+x^2)$$  I have no clue how to solve this since it is obvious there is no way to cancel out either $A$ or $B$ to get the other variable. Please guide me.  Thank you. Material setings in properties window is missing