Speed of the rotating block
How can tangential acceleration from a radial force be explained?
Can you flank with a reach weapon? The Variant: Flanking rules in the DMG (page 251) require adjacency, but is the intent that the Enemy has combatants on opposite sides and thus someone with Reach (and using the reach) could still flank even if not directly adjacent?  Looking for both RAW as well as Intent of the flanking rule. SQL Server compatibility with New TLS Standards Should I keep my swap file on an SSD drive? I'm considering getting an SSD drive to run as the primary OS partition.  As I understand, this should provide a substantial improvement in performance.     My question is this: Should I leave the swap file on that drive?     The swap partition will be largely random seeks and so should benefit from the speed.  On the other hand, it will be constantly written to which will wear out the drive faster. Does C1 code coverage analysis exist for Ruby? I'm currently using  to get C0 code coverage analysis for a rails project that I'm working on.  However, those results are practically meaningless- I have 100% coverage according to rcov (as it only covers C0 analysis) and I've barely written half the test cases for the functionality that exists thus far.  I'm used to the useful results from the code coverage in Visual Studio 2008 Team, which has C1 coverage.  Are there any tools that provide similar coverage for ruby? How should I add users non-interactively? I have a set of users I need to add to a new system as part of a BASH script that preps my server. How can I non-interactively add the user, create their home directory, set the group, and enter a default password?  For example, if I needed to add the following users, how would I go about that?  user: node password: spoon group: ultraMegaPermissions  user:serve password: spoot group: sortaNotMega  user:watcher password: spoogle group: notMega Show that G is a group, if G is finite, the operation is associative, and cancellation law holds Let $G$ be a non-empty finite set with an associative binary operation so that cancellation law holds, i.e. $ab=ac$ or $ba=ca$ implies $b=c$, for any choices of $a,b,c$ in $G$. Assume that there is an identity element $e$ in $G$. Show that $G$ is a group.  Proof: To show $G$ is a group, conditions must hold. Suppose that $ab=ac$, then $b=eb=(a^{-1}a)b =a^{-1}(ab)=a^{-1}(ac) =(a^{-1}a)c=ec=c$. So left cancellation holds in $G$.  2) Suppose $ba=ca$, then $b=be=b(aa^{-1}) =(ba)a^{-1}=(ca)a^{-1} =c(aa^{-1})=ce=c$. So right cancellation holds in $G$.  3) If $a$ exists in $G$ then $aa^{-1}=a^{-1}a=e$, where $a$ is an inverse of $a^{-1}$. Since inverses are unique, $(a^{-1})^{-1}=a$.  4) Let $x$ be the inverse of $ab$. Then $(ab)x=e$. By associativity we have $a(bx)=aa^{-1}$. Through left cancellation we have  $bx=a^{-1}bx=ea^{-1}=b(b^{-1}a^{-1})$ and $x=b^{-1}a^{-1}$.  Thus $(ab)^{-1}=b^{-1}a^{-1}$. So all conditions hold, $G$ is a group.  Is this proof correct? I know to show $G$ is a group these conditions have to be met. This is all I have to show right? Trying to dual boot Ubuntu 14.10 with Windows 10, last one not detected How does pointing a CNAME on my domain to a service-provider's server enable them to offer customized services? Can I install any iOS version I wish by picking and choosing which firmware to restore? I'm trying to downgrade my iPhone from the current iOS to an older one, as per .  But every time I try, I always receive this error:     The iPhone could not be restored. This device isn't eligible for the requested build.     I have tried many times with and without DFU mode. Any ideas regarding this? Black holes and positive/negative-energy particles reCaptcha v1 is shutting down on March 31, but SEDE still uses it According to this , I thought the new recaptcha API was used network-wide. Though today, when going to  (which for whatever reasons never recognized me automatically), I got this message instead of a usable captcha image.   V1 Unsupported Please direct siteowner to   (Doing a second try doesn't show this message anymore, and the recaptcha v1 works as intended.)  According to , the reCAPTCHA v1 API will stop working on March 31, 2018:  What happens to reCAPTCHA v1? Any calls to the v1 API will not work after March 31, 2018. Starting in November 2017, a percentage of reCAPTCHA v1 traffic will begin to show a notice informing users that the old API will soon be retired. Most websites around the world have already switched to reCAPTCHA v2, where humans pass effortlessly. With our advanced risk analysis engine, reCAPTCHA v2 can effectively separate humans from bots and always stay ahead of the attackers. If your site still uses reCAPTCHA v1, please upgrade to reCAPTCHA v2 immediately. We no longer support reCAPTCHA v1. Any calls to the v1 API will not work after March 31, 2018. Please register a new key and upgrade to v2.  I'm really hoping this will not take  to fix, because we've only got three and a half weeks left! FM Transmitter oscillation problem I've been trying to get this simple FM transmitter to work over the past few days and I could use some help in a few areas.      First iteration was on a breadboard with all parts included.  The exception being I didn't have a 0.1uH coil handy but I had another coil rated at 0.7uH (using my LCR meter).  I also didn't have a C4 value of 4.7pF but I had a 10pF value.  I figured I could just tune it later.  I hooked a scope up to it and got no oscillation.  I tried connecting the probe to the gate and the collector separately and together.  Still no oscillation.  Second iteration.  I removed the audio component of the circuit.  Essentially everything to the left of C2.  I had gotten that working no problem anyway so I figured I would concentrate on the oscillator.  This time I tried different values for the inductor ranging from 20uH to 1mH and different fixed values for the variable cap (10pf, 20pf, 30pf).  These were all ceramic caps. No love.  Third iteration. I tested the transistor to make sure that wasn't the issue.  Seems fine.  PN2222A variety. (Also tried 2N3904 and BC547). I then modeled this up on a piece of perf board.  I even found a SMD inductor of 0.1uH so now I thought I would be good.  Tested all the pieces on the meter before installation. Still nothing. I'm not seeing anything on the spectrum analyzer either.  Questions:   Do you think my benchtop power supply is causing a problem?  All the various versions of this type of FM transmitter circuit on YouTube and the Internet all seem to use a battery.  Any chance the 60Hz main power is messing with things?  I've put .1uF and higher caps on the power rails. I have a 200Mhz SIGLENT SDS1202X-E scope.  I've built and tested other oscillators up to a few MHz before with no issues.  Any thoughts on that being the issue?  I would expect to see something on the scope right? Any chance the probe is dampening the oscillations?     I know there are a lot better FM transmitter circuits out there I was just experimenting with this (and others like it) and couldn't get any to work. Is it possible to do something like this  #ifdef SOMETHING #define foo // #else #define foo MyFunction #endif   The idea is that if SOMETHING is defined, then calls to foo(...) become comments (or something that doesn't get evaluated or compiled), otherwise it becomes a call to MyFunction.  I've seen __noop used, but I don't believe I can use that.  EDIT(s):  I don't think I can really use a macro here, because MyFunction takes a variable number of arguments.  Also, I'd like to make it so the arguments are NOT evaluated!  (So doing something like commenting out the body of MyFunction doesn't really give me what I need, as the arguments will still be evaluated) "[somebody]'s theme" vs "[somebody] theme" — Saxon genitive dillema When is it required to use 's in phrases like below (examples taken from Wikipedia)?   James Bond theme 007 theme Boba Fett motif Droids motif Yoda's theme ...   Are there any rules for eliding Saxon genitive?  How does the situation change if we have something instead of somebody? Wrap text at any point if normal hyphenation not possible I have data (generated from a database, not manually typed in) that mostly fits into a table cell with fixed width, but sometimes overflows because there are long words for which no hyphenation is found.  The problem can be demonstrated with the following example:  \documentclass{article} \usepackage[utf8]{inputenc} \begin{document} \begin{tabular}{|p{1cm}|p{4cm}|} 1 &amp; Cell where normal hyphenation is possible ÄÖÜ \\ 2 &amp; CellwherenormalhyphenationisnotpossiblebutshouldwrapinsteadofoverflowÄÖÜ \end{tabular} \end{document}   My requirements are:   Text never overflows the cell (assuming some minimum width such that at least a handful characters have place) First priority measure to achieve 1. is the normal hyphenation If 2. fails, it is allowed to break the word at any character, so fill the line and break just before overflow would happen (disregarding normal hyphenation rules)   In the example, the overflow in cell 1 is prevented by measure 2., the normal hyphenation. The second cell overflows. I would like to have this cell treated by measure 3.  For the answer please consider:   Package seqsplit didn't help me The custom macro \wrap proposed in the answer to  comes near my wish, but can't handle the non-ascii characters ÄÖÜ (independent if they are input with utf8 input encoding or with \"A\"O\"U) As the text comes from a database, no manual editing of the cell content is wanted.   One of my ideas was to insert \linebreak[0] after every character, to tell LaTeX that a break can be made if no better opportunities exist. But this doesn't work like intended.  Thanks for your suggestions! The question is if you have a situation where one of the singular values is equal to 0 in a singular value decomposition of a matrix, how to do you procede to find the column vector of U corresponding to this singular value?   Usually I found the columns of U with this relation, so let's say that we refer to $\vec{u_2}$ as the U column vector corresponding to singular value equal to 0:  $\vec{u_2} = (1/s_2)Av_2$  Now the as we can see the 0 is in an illegal place, since you can't divide by zero. But if you move it to the left side, I still can't quite see how to find the column of U corresponding to it. Any suggestions?  Here is an example of a matrix that provided this specific challenge  $ A = \left(\begin{array}{rrr} -3 &amp; 1 \\ 6 &amp; -2 \\ 6 &amp; -2 \end{array}\right). $  $ \lambda{_1} = 90$,  $\lambda{_2} = 0$,  $s_1 = 3 \sqrt{10}$,  $s_2 = 0$,  How can one find $\vec{v_2}$ when $\lambda{_2} = 0$? In this case, you know that the eigenvectors of $A^{t} A$ are orthogonal, solve for $\lambda{_2}$ and find the eigenvector if it's orthogonal to the eigenvector corresponding to the first eigenvalue you have your solution.  So we end up with the following normalized column vectors for V, which we can see are orthogonal:  $ \vec{v_1} = \left(\begin{array}{rrr} -3/\sqrt{10} \\ 1/\sqrt{10} \\ \end{array}\right). $  $ \vec{v_2} = \left(\begin{array}{rrr} 1/\sqrt{10} \\ 3/\sqrt{10} \\ \end{array}\right). $ How do I distinguish between a command, utility, or builtin for getting documentation? I'm running Bash scripting, but sometimes I get confused which of these commands I use belong to who. Sometimes man xxx works, sometimes doesn't, so I use --help or info, mostly one of these works to show description of the command. Can anyone tell me how I would know what command belongs to what? Bash builtin, GNU utility, etc. Integrating $\int^{\infty}_0 e^{-x^2}\,dx$ using Feynman's parametrization trick Is $[0,1]$ a countable disjoint union of closed sets? How can I redirect the user from one page to another using jQuery or pure JavaScript?