What is the cause of the surface tension of the liquids? How to know the direction of tension force on the free surface of the liquid?   I know that the surface tension is the force acting normally per unit length of the imaginary line drawn on the free surface of a liquid, but don't have any idea about the cause of the surface tension. More over I don't know the direction of the tension force i.e. where it towards liquid or away from the liquid.  Any idea or help will be greatly appreciated!
A text says:     The surface tension of a liquid results from an imbalance of intermolecular attractive forces, the cohesive forces between molecules:   A molecule in the bulk liquid experiences cohesive forces with other molecules in all directions.   A molecule at the surface of a liquid experiences only net inward cohesive forces   If this is the case: Why is surface tension considered or experienced as a force parallel to the interface while it is so obvious that it must be perpendicular to it?
I'm not a resident of USA. But I work on a cruise ship which required me to have C-1/D visa. I am leaving USA and traveling to Mexico but I will have a connecting flight somewhere in another US airport with 1-2 hours waiting for connecting flight to Mexico.   Do I need B1/B2 visa for that? Or my transit visa C-1/D will be enough as long as I am leaving USA? Let $n$ is a natural number. Prove that $$\left\lfloor\frac{n}{1}\right\rfloor+\left\lfloor\frac{n}{2}\right\rfloor+....+\left\lfloor\frac{n}{n}\right\rfloor+\left\lfloor{\sqrt{n}}\right\rfloor$$   is even.   I used induction and the inequality $$x-1&lt;\lfloor{x}\rfloor\le{x}$$ to prove it.  Is there any other, nicer way to do it? Blender 2.8 - AWS EC2 command line EEVEE render I have been trying to get this to work for a couple days now. I have an EC2 P2 instance with NVIDIA CUDA configured by default, its a Deep learning Ubuntu AMI. This OS does not have a GUI so everything is via terminal.  I downloaded Blender's 2.8 TAR file for Linux and set it up on the EC2 instance. And ran the following command from the directory where the TAR file is extracted:   ./blender -b -noaudio /home/ubuntu/file.blend --render-output . --engine BLENDER_EEVEE --render-format PNG --verbose 4   All I see in the output is this:  Blender 2.80 (sub 75) (hash f6cb5f54494e built 2019-07-29 17:17:04) found bundled python: /mnt/blender/blender-2.80-linux-glibc217-  x86_64/2.80/python Read blend: /home/ubuntu/file.blend  Blender quit   Don't know why its quitting but I am unable to debug this any further. Any help would be appreciated.  UPDATE: As per @rjg's recommendation, ran the following command:  ./blender -b -noaudio /home/ubuntu/file.blend --render-output . --engine BLENDER_EEVEE --render-format PNG -f 1 --verbose 4   Got the following error:  Blender 2.80 (sub 75) (hash f6cb5f54494e built 2019-07-29 17:17:04) found bundled python: /home/ubuntu/blender/blender-2.80-linux-glibc217-  x86_64/2.80/python Read blend: /home/ubuntu/file.blend Unable to open a display Aborted (core dumped) Arrays, linked lists and other data structures in cmd.exe (batch) script I read this story 30+ years ago in grade school. A man crashes on an alien planet. He has a small amount of water and accidentally spills some, and the planet replicates it but it must destroy part of itself to do so.  The man then finds some stale crumbs in his pocket, puts them in a trough, and the planet replicates them as well, but it's disgusting to eat. The man eventually decides that his situation is hopeless, so he lays down to die on a table in a hot room and thinks he can at least give back to the planet some of the nutrients it sacrificed for him. He falls asleep, and when he awakens, he has been transformed into an alien creature that is perfectly suited and adapted to live on the planet without discomfort to himself or damage the planet. "Friendly" terminal color names in shell scripts? I'm aware of libraries in languages such as Ruby and Javascript to make colorizing your terminal scripts easier by using color names like "red".  But is there something like this for shell scripts in Bash, or Ksh, or whatever? If $G/Z(G)$ is cyclic, then $G$ is abelian Continuing my work through Dummit &amp; Foote's "Abstract Algebra", 3.1.36 asks the following (which is exactly the same as exercise 5 in ):     Prove that if $G/Z(G)$ is cyclic, then $G$ is abelian. [If $G/Z(G)$ is cyclic with generator $xZ(G)$, show that every element of $G$ can be written in the form $x^az$ for some $a \in \mathbb{Z}$ and some element $z \in Z(G)$]      The hint is actually the hardest part for me, as the quotient groups are somewhat abstract. But once I have the hint, I can write:  $g, h \in G$ implies that $g = x^{a_1}z_1$ and $h = x^{a_2}z_2$, so \begin{align*}gh &amp;= (x^{a_1}z_1)(x^{a_2}z_2)\\\  &amp;= x^{a_1}x^{a_2}z_1z_2\\\ &amp; = x^{a_1 + a_2}z_2z_1\\\ &amp;= \ldots = (x^{a_2}z_2)(x^{a_1}z_1) = hg. \end{align*} Therefore, $G$ is abelian.  1) Is this right so far?  2) How can I prove the "hint"? How to prove that $A_5$ has no subgroup of order 30? How can I pad a String in Java? Is there some easy way to pad Strings in Java?  Seems like something that should be in some StringUtil-like API, but I can't find anything that does this. Prove if $|z| < 1$ and $ |w| < 1$, then $|1-zw^*| \neq 0$ and $| {{z-w} \over {1-zw^*}}| < 1$ Prove if $|z| &lt; 1$ and  $ |w| &lt; 1$, then $|1-zw^*| \neq 0$ and $| {{z-w} \over {1-zw^*}}| &lt; 1$Given that $|1-zw^*|^2 - |z-w|^2 = (1-|z|^2)(1-|w|^2)$I think the first part can be proven by saying $|1-zw^*| = 0$ if and only if $zw^*$ = 1.  And given the conditions that cannot be true. However I don't know if this part is right. Exit strategies for "chameleon questions" I'm not sure if there's already an existing term for this, so I'm inventing my own. (tl;dr: I call them &quot;chameleon questions&quot; because they change every time you submit or edit an answer.  If you're already intimately familiar with the phenomenon, please skip past the first set of bullet points to where I ask for recommendations.)  I think many of us have experienced this on occasion:  You open up a narrow-looking question, usually dealing with some specific error message.  The question probably contains a snippet of sloppy but not quite awful code; code indicating that the author, typically a new/low-rep user, possibly a , doesn't really know what they're doing.  I'm not trying to be condescending here, they're probably very intelligent and hardworking, but in this specific case, they're clearly in way over their head.  However, as a question, it's not really too bad.  The goal and problem are both clearly stated.  The code is formatted (sort of).  Mort was polite and checked their spelling.  The question looks answerable, although from a rep perspective* it's an obvious dead-end, it's had maybe 3 views in the past 30 minutes.  So you decide, you know what, this person took the time to write up the question properly, they deserve an answer, put on your good citizen hat and throw them a bone.  You slog through the ugly code, find the offending line, direct their attention to it and explain why it's wrong and how it needs to be fixed.  Later, they leave a comment saying that yes, that was indeed the problem and your answer helped them fix it (great!).  Oh, but, now there's another problem (uh-oh...). Something else is broken.  After letting out a long sigh, you read the comment and/or edited question, roll up your sleeves, and write up Take 2, hoping that's the end of it.  And of course it's not the end.  Now maybe the error is gone, but it's not doing what it's supposed to.  If you're anything like me, your patience is now starting to wear thin. It's lousy code and you didn't volunteer to help them rewrite their whole app.  And of course, the question still only has 12 views, and nobody has upvoted either the question or your answer, including the person you're helping, so this is turning out to be a genuinely thankless task in all respects.  Welcome to &quot;Family Tech Support&quot;, Web 2.0 Edition.   * Which is of course just an arbitrary number that none of us care about. Not really, anyway. Not very much, at least.  So, here's where I get to my question.  At this point, do you:  Leave a comment, stating as politely as possible that you've done your best to help them answer the original question they asked, and if they have a new problem then they should start a new question?  (I did this once, and actually ended up with an accept, but I felt kind of guilty afterwards, I don't think anybody answered their 2nd question).  Bite the bullet and edit your answer a 3rd, 4th, 5th time, however many times it takes to resolve their issue, knowing full well that they may not even remember to accept the answer once you're done? (I may work for free on SO, but that doesn't mean my time is worthless.)  Just abandon the question, hoping that it will force Mort to start thinking for himself?  Something else?   I've tried all three of the above and none of them ever quite feel right. I do want to help, but at the same time there are a lot more &quot;lucrative&quot; questions I could be answering. And I don't mind spending a lot of time on an answer either, if the question is interesting or important to me, but debugging is dull work. I'd prefer not to reference specific questions here; I'm pretty sure that this is a shared experience, and my objective isn't to point fingers at &quot;misbehaving&quot; members.  I'm more looking for some practical advice on how to dig myself out of these pits of despair. Anybody have any other ideas? I need to find node voltage at A. This seems like a trivial question, but when I set up the resistive voltage divider equations they are not equal to each other. Am I doing something wrong?  My equations are \$V_A = V_1(R3/(R3+R1)) = V_2(R3/(R3+R2))\$      I tried solving this problem with an LTSpice simulation and with the superposition method, but my answers did not match (although very close to each other). Is this because the simulator uses an approximation? Can someone compare results? Why does the SUID bit have no effect when applied to directories in Linux? I clearly see that I can set it with 'chmod u+s'. But why does it not have "any" effect. What is the reason for implementing a way to SET it but not implementing any effect? Can you flash any android device with "fastbood flash" command (of the adb)? Why is it so hard to find the roots of polynomial equations? The question that follows was inspired by  question:  When trying to solve for the roots of a polynomial equation, the quadratic formula is much more simple than the cubic formula and the cubic formula is much more simple than the quartic formula.    That the general solutions to various polynomial equations are so complex and difficult to derive seems to suggest a fundamental limitation in the problem solving capabilities of the mathematical machinery. Does this intuition of mine make any sense? What should I make of it? Why is it that with each successive degree in a polynomial equation, the solution becomes so much more complex? Can I gain some intuition about what makes finding the roots so hard? According to the : "there is no general algebraic solution—that is, solution in radicals— to polynomial equations of degree five or higher." What is so special about the quintic that makes it the cut-off for finding a general algebraic solution? How to find Windows 7 File Transfer History? I have two arbitrary lines in 3D space, and I want to find the distance between them, as well as the two points on these lines that are closest to each other.  Naturally, this only concerns the skew case, since the parallel and intersecting cases are trivial.  I know how to find the distance, as the question was asked before and answered .  I haven't found a good explanation on how to find the two points that determine that distance, though.  So specifically, given two lines  $$L_1=P_1+t_1V_1$$ $$L_2=P_2+t_2V_2$$  I would like to find two points $X_1$ on $L_1$ and $X_2$ on $L_2$ such that the distance between $X_1$ and $X_2$ is minimal. What is the problem with nested environments using \BODY (environ package)? This question led to a new package:      I want to define some environments, which place their content into multiple different other environments. To access the contents I used the environ package, which introduces the \BODY command. However at some point pdflatex seemed to be stuck in an infinite loop.  I reduced it to a minimal example:  \documentclass{article} \usepackage{environ}  \NewEnviron{assertion}{Assertion: \BODY} \NewEnviron{outerassertion}{\begin{assertion}\BODY\end{assertion}}  \begin{document}  \begin{assertion} test \end{assertion}  \begin{outerassertion} test2 \end{outerassertion} \end{document}   Any ideas how to work around this problem? I guess, the problem is with the \BODY command since everything works fine as long as I use it in only one of the new environments. Why did the limit of power change from wizard/witch to wand? So in the first 5 or 6 books, it was very clear that the wand chooses the wizard and the power/level of the spells the wizard produces is based on the knowledge and skill of the wizard.  This is referenced by people constantly being telling Harry that he wasn't skilled enough to perform certain spells, or Bellatrix telling Harry that he needed to mean the Cruciatus curse for it to be effective.  However, in the 7th book, this entire idea is changed to the wand being the thing that's powerful and regardless of the wizard's/witch's skill or knowledge, he/she could still perform a very advanced spell if it's something the wand could handle.  Goyle accidentally creating a fire serpent is something that instantly comes to mind from the movies(I don't remember if that happened in the book).  So, my question is, what actually holds the power, the wizard/witch, or the wand? is the group of rational numbers the fundamental group of some space?