Analogue of $\varepsilon_0$ for gravitational mass?
Newton's Law of Graviation: Why $G$ and not e.g. $\dfrac{1}{4\pi G_0}$?
Is volunteer work allowed in the US while visiting under the VWP or a B1/B2 visa? I am going to Santa Monica for 4 weeks to polish my English in July and would like to volunteer at the Planetary Society located in Pasadena.  I am a Swiss citizen and have a biometric passport. However, I don't have any special visa, as there is no visa needed for the school I am attending and using the Visa Waiver Program, I am allowed to stay up to 90 days in the US.  Am I allowed to do volunteer work during my stay? If $X$ is an orthogonal matrix, why does $X^TX = I$? It's not immediately clear to me why this is true. My notes say that putting $n$ orthonormal vectors $ v_1, ..., v_n$ in the columns of $X$ gives $X^TX = I$, and it follows from this that the rows of $X$ are orthonormal.   Can you explain this better to me? I tried the $2\times 2$ case, but it isn't clear to me why this is true. $t^3$ is never equal to Let $t$ be a real number such that $t^2=at+b$ for some positive integers $a$ and $b$. Then for any choice of positive integers $a$ and $b$, $t^3$ is never equal to: (A). $4t+3$ (B). $8t+5$ (C). $10t+3$ (D). $6t+5$  We have $t^3 = at^2+bt$ and so for (A) we have $t^3 = 4t+3 = 4(at^2+bt)+3$. I don't see how to continue since this is a cubic equation. Is there an easier way of finding a contradiction? Disable Tabbing in Firefox 3, Chrome 4 and IE8? Tabbed Browsing may be nice for reading news sites in one sitting, but I still think they are a usability nightmare if you need to keep the page open for a long time, e.g., for testing it while developing or as a reference for something.  The nice thing about the Windows Taskbar (before Windows 7 ) is that it's easy and natural to remember where things are. I can have 30 tabs in it, but because I know what each one is, I know where I have to click to open something - it's the most efficient way of working I've encountered so far.  Sadly, Tabbed Browsing completely breaks this efficiency because it is not possible to specifically click on a tab in the taskbar, I have to click on the browser, search the tab and then click it, which means at least 2 clicks.  Long story, short question: Is there an extension or setting to completely disable tabbing on Firefox 3, Chrome 4 and Internet Explorer 8 and have one Window/Taskbar entry for each open page? I know that in Chrome I can just drag a tab out of a Window to create a new one, but if there is a general way, that would be easier.  Edit: IE8 conveniently offers an option for that: Tools - Options - Tabs - Enable Tabbed Browsing. What do we mean by hyperparameters? How can I get multiple stacked plots (ybar stacked, stack plots=y) in one diagram, such that there are multiple stacked bars for the same x-coordinate, each slightly shifted? Is there a way to reset pgfplot's zero levels after an \addplot command, such that the next \addplot[xhshift=...] doesn't add something to the current stack, but rather starts a fresh stack?  FWIW, overlaying two plots with scale only axis won't help; I need this to work with groupplot Finding a permutation, and number of, from powers of the permutation Classifying whether a collection of objects is a set I'm wondering whether or not there is a definite criterion for determining whether a collection of objects is a set. In the literature, I've recently encountered some obscure examples (in Riemann Surface Theory, to be precise) of naturally-arising collections of objects which are not sets.   Here is some pseudo-rigor to make the question more precise:   Let $S$ be a collection of objects. Is there some property $P$ so that $S$ is a set iff $S$ has property $P$? In GLM regression I have always been told to set the reference level of categorical/ordinal/dummy variables to the level with the most exposure (level with most data), because this somehow makes the model more stable. Is there any statistical reason behind this, or just historical practice without statistical reason?  I can understand that one wants a "baselevel" (reference level) in the model that are most likely to be correct, but if you are not sure about the other levels, then they surely should not be included in the regression in the first place? Full width image in beamer? Syntax highlighting in app differs from normal web view Other users have been leaving me angry and hostile comments accusing me of plagiarism and saying that I'm a liar and I should stop stealing answers. But I have only been copying content from other sites, not taking answers from other users.   I don't understand what is wrong here. Shouldn't we be focused on building all the content and knowledge in a single place, much like Wikipedia does?  What does it matter that I copy and paste content I've found elsewhere so long as the question gets an answer? Can I safely charge my laptop with a non-standard, third-party charger? I have a Toshiba Satellite laptop. My charger has stopped working.  I have access to a Lenovo charger. Can I use this charger on my laptop? Does Process Builder run with System permissions or User permissions? Regarding field-level security, does Lightning Process Builder run as system-level permissions or user?  That is:   Can I trigger an update to a field that the current user cannot edit? Can I filter based on a field the current user cannot read? The laptop is dual booting with windows 7 and ubuntu 11.10.  For 11.10 to boot, I had to add 'nolapic' in GRUB boot options.  I downloaded 12.04LTS LiveCD yesterday and made a CD and a bootable USB stick.  With both USB and LiveCD, occasionally I can boot into 12.04.  But many times, the boot process stuck at some point.  For USB boot, sometime it works.  But other times, it seems to stuck right after seeing the message:  NMI watchdog enabled. takes one hw-pmu counted [0.408590] #2   The number in [] changes.  Some times it stuck at #2, and sometimes at #3.  For LiveCD boot, sometime it works.  But when it stuck, it stuck at different places.  At times, the boot process go directly to a blank screen with a blink '_' at up left corner.  Sometime it went a bit further, after showing options to try/install ubuntu then stuck with a blank screen with blink '_'.  Anything I can do to get around of this? Integral of $\sin(e^t)dt$ Let $f(x) = \int_x^{x+1} \sin(e^t)dt$. Show that $$ e^x|f(x)| &lt; 2 $$ and that $$ e^xf(x) = \cos(e^x) - e^{-1}\cos(e^{x+1}) + r(x) $$ where $|r(x)| &lt; Ce^{-x}$ for some constant $C$.  I can do the first part easily. Integration by parts gives us $$ f(x) = \frac{\cos e^x}{e^x} - \frac{\cos e^{x+1}}{e^{x+1}} - \int_{e^x}^{e^{x+1}} \frac{\cos u}{u^2}du, $$ so substituting $\cos u = 1$ and $\cos u = -1$ gives \begin{align*} \cos e^x - 1 + \frac{1}{e}\left(1- \cos e^{x+1}\right) &amp;\leq e^xf(x) \leq \cos e^x + 1 - \frac{1}{e}\left(\cos e^{x+1} + 1\right)\\ -2 &amp;&lt; e^xf(x) &lt; 2 \end{align*} So that $e^x|f(x)| &lt; 2$.  I get stuck on the second part, though. From integration by parts, I have $e^xf(x) = \cos e^x - e^{-1}\cos e^{x+1} - e^x\int_{e^x}^{e^{x+1}} \frac{\cos u}{u^2}du$, so it reduces to showing that $$ \left|\int_{e^x}^{e^{x+1}} \frac{\cos u}{u^2}du\right| &lt; Ce^{-2x} $$ for some constant $C$. However, I always end up with a constant for $Ce^{x}$ rather than for $C$. How to dump a man page? How to get a drive formatted with exfat working? In Ubuntu 13.04 there was an option to use the PPA by Relan in order to get ExFat functionality. Seeing that in Ubuntu this functionality is now available from the repositories without the PPA I tried this but failed to make it work.  So my question is how do I enable exfat support? How to set up USB for Virtualbox? If $x_1,x_2,\ldots,x_n$ are the roots for $1+x+x^2+\ldots+x^n=0$, find the value of $\frac{1}{x_1-1}+\frac{1}{x_2-1}+\ldots+\frac{1}{x_n-1}$ Let $x_1,x_2,\ldots,x_n$ be the roots for $1+x+x^2+\ldots+x^n=0$. Find the value of   $$P(1)=\frac{1}{x_1-1}+\frac{1}{x_2-1}+\ldots+\frac{1}{x_n-1}$$   Source: IME entrance exam (Military Institute of Engineering, Brazil), date not provided (possibly from the 1950s)  My attempt: Developing expression $P(1)$, replacing the 1 by $x$, follows $$P(x)=\frac{(x_2-x)\cdots (x_n-x)+\ldots+(x_1-x)\cdots (x_{n-1}-x)}{(x_1-x)(x_2-x)\cdots (x_n-x)}$$    As $x_1,x_2,\ldots,x_n$ are the roots, it must be true that   $$Q(x)=(x-x_1)\cdots(x-x_n)=1+x+x^2+\ldots+x^n$$ and  $$Q(1)=(1-x_1)\cdots(1-x_n)=n+1$$ Therefore the denominator of $P(1)$ is  $$(-1)^{n} (n+1).$$ But I could not find a way to simplify the numerator.  Another fact that is probably useful is that  $$1+x^{n+1}=(1-x)(x^n+x^{n-1}+\ldots+x+1)$$ with roots that are 1 in addition of the given roots $x_1,x_2,\ldots,x_n$ for the original equation, that is  $$x_k=\text{cis}(\frac{2k\pi}{n+1}),\ \ k=1,\ldots,n.$$  This is as far as I could go...    Hints and full answers are welcomed.