Can pressure be negative?
Define Pressure at A point. Why is it a Scalar?
failed to fetch security undermined error [IP: 91.189.91.38 80] in ubuntu 20.04 I'm completing a problem set, one problem for which I literally have no idea what to do on. The graders would prefer to have a physical copy of the problem so I thought it best to include the ¯\_(ツ)_/¯ emoji as my answer, instead of something like "Dunno" or "No idea."  Option #1 is to include an image.  Beyond that I actually don't understand how this emoji works. The middle character is Japanese kana "tsu" and proves problematic - TeX wants it in math mode then renders "?" when it is. Happened on , fwiw. In particular I voted to reject it, then visited to add comment and vote to close, and wanted to add a  tag, but couldn't because had to wait to see the fate of the edit. Query standard input of lightning-input I want to query standard HTML textarea which is wrapped by lightning-textarea. How can I get it?  &lt;lightning-textarea name=&quot;secret_field&quot; label=&quot;Secret&quot; value={secretFieldValue}&gt;&lt;/lightning-textarea&gt; Migrate database from Postgres to MySQL Looking at the kids which - or that/who? We look at the kids which/that/who skillfully use tablets with the help of their small fingers and we understand that to surprise the younger generation will be more difficult each year.   Is the relative pronoun which acceptable here, or does it look totally out of place, because it befits a "non-restrictive relative clause" more?   It seems to me that the pronoun that looks best in the bolded position, with who an acceptable second choice. But it's hard to pin down why. I don't understand how to use Fermat's little theorem to find remainders e.g if we are asked to find remainder of $50^{50}$ on division by $13$, what is a and what is $p$ in the formula?  Also I wanted to check can we use both congruence classes as well as Fermat's little theorem to find such remainders? How would be write $50^{50}$ on division by $13$ in terms of congruence classes to find the remainder?  I don't exactly understand what a congruence class is, what does it tell us and how is it related to this? Where in the world is tikzlibraryhobby.code.tex? I was trying to reproduce Claudio Fiandrino's answer to .  However, I do not have the hobby package by Andrew Stacey in my local distribution.  After reading  and , I looked at the latest  (build on December 7, 2012) but could not located the hobby package in it.  I found  but do not know where each file is supposed to go in my distribution.  How do I add the hobby package? In general, what would be the easy way to get any new TikZ package installed in a Mac?  EDIT:  I have used the drag-and-drop (mac) method as described below.  (1) Drag pml3array.sty file to /Users/Username/Library/texmf/tex/latex folder. (2) Drag hobby.code.tex file to /Users/Username/Library/texmf/tex/generic/pgf/math folder. (3) Drag pgflibraryfpu.code.tex to /Users/Username/Library/texmf/tex/generic/pgf/libraries folder. (4) Drag tikzlibraryhobby.code.tex to /Users/Username/Library/texmf/tex/generic/pgf/frontendlayer/tikz/libraries folder.  I no longer get the hobby cannot be found error message.  But, is this correct? Position of a relative clause before/after a verb I'm not sure about the sentence structure below:  All kinds of problems arise that smaller animals or plants do not have to cope with.  It looks like that works as a relative pronoun for all kinds of problems, but I couldn't find such usage in my dictionary or online. This sentence could be divided into  There are all kinds of problems. Smaller animals or plants do not have to cope with all kinds of problems.  But, I can't figure out where 'arise' fits. If you have any thoughts, please share them. "Compared with" vs "Compared to"—which is used when? Is only one of them correct? Are they used in different situations? Or are they interchangeable? Show that all horses are of the same color. Im trying to understand the solution about this, and all the other solutions are.. a bit weird for me and dont answer all my questions!  Reference :   Im using the answer there as reference, but my understanding is a bit different!     Find the error in the following proof that all horses are the same   color. CLAIM: In any set of h horses, all horses are the same color.      PROOF: By induction on h.      Basis: For h = 1. In any set containing just one horse, all horses   clearly are the same color. Induction step: For k > I assume that the   claim is true for h = k and prove that it is true for h = k + 1. Take   any set H of k + 1 horses. We show that all the horses in this set are   the same color. Remove one horse from this set to obtain the set H1   with just k horses. By the induction hypothesis, all the horses in H,   are the same color. Now replace the removed horse and remove a   different one to obtain the set H2 . By the same argument, all the   horses in H2 are the same color. Therefore all the horses in H must be   the same color, and the proof is complete.   Here's what i have come up with :  Suppose a set of 1 horse. $H_a = { horse_{1} }$  Obviously, all the horses in set $H_a$ are the same, since theres just 1 horse.  So using that as the Basis of the induction we can proceed and try to prove its true for $N$ horses.  -- I dont fully understand the part below   As an example : set $H_0$ :   $H_0 = { horse_{1}, horse_{2}, horse_{3}... horse_{n} }$  In my understanding, its because, I can make a subset  formed by 1 horse :  $K_1  = {horse_{1}}$ $K_2  = {horse_{2}}$ ...  I don't get it. I clearly know that this proof is a lie.  And for me, its because you cant claim theres a relation on a set with size $&gt;= 2$ , since :  $H_1 = { horse_{1}, horse_{2}}$  Theres nothing that says $horse_{1}$ equals $horse_{2}$. The basis was for one horse. But that alone is not a proof.  So what should I do ? I've got a PDF that is automatically generated from a certain piece of software, that I want to include in the report I'm writing. I'm using pdfpages which gets the job done elegantly, but the problem is, the PDF has a lot of white space around the actual content (which is a graphics) and I always have to do some tedious post-processing of the automatically generated document so that it fits well in my report. Changing the output of the software to eliminate the white space is not an option (or at least, would be much more trouble than it's worth).  I checked the pdfpages , but wasn't able to find an option that does that. Ideally, I'd like to be able to set margins from each direction, and the PDF is then cropped accordingly and included.  What other options do I have to control what portion of the included PDF is visible in the final document? For all $X \geq 1$,$\sum\limits_{1 \leq n \leq X} \mu(n) \left[\frac{X}{n}\right] = 1.$ I'm currently sitting with the following number theory problem:  Prove that for all $X \geq 1$, $$\sum_{1 \leq n \leq X} \mu(n) \left[\frac{X}{n}\right] = 1.$$  A few ideas I have tried: Using that $[x]=x - \{x\}$ which I couldn't make out to bring anything. Switching around on the summation variables, like $$\sum_{d \leq N} \mu(d) f\left( \frac{n}{d} \right) = \sum_{d \leq N} \mu \left( \frac{d}{n} \right) f(d)$$ but that didn't seem to bring anything.  I tried writing out the first few terms, which give $$\mu(1) [X] - \left[\frac{X}{2}\right] - \left[\frac{X}{3}\right] - \left[\frac{X}{5}\right] + \left[\frac{X}{6}\right] - \left[\frac{X}{7}\right] - \left[\frac{X}{8}\right]$$ but I can't seem to find a system where it simply reduces to one!  What do you think? How do I use SQL's GETDATE() and DATEADD() in a Linq to SQL expression? If I have a Linq to SQL expression like this:    from subscription in dbContext.Subscriptions  where subscription.Expires &gt; DateTime.Now select subscription   I want this to to use the SQL Servers GETDATE() function instead of the time of the machine running the C# program.  The next question would be how to translate this:  DateTime.Now.AddDays(2)   to this:  DATEADD(dd, 2, GETDATE()) Diagonalizable matrix with parameters $$     \begin{bmatrix}     -2 &amp; -2 &amp; 0 &amp; 0 \\     -b &amp; -b &amp; 0 &amp; 0 \\      0 &amp; 0 &amp; -4 &amp; 4 \\      0 &amp; 0 &amp; b &amp; -b \\     \end{bmatrix} $$  I have this matrix and I need to find the values for $b$ that this matrix won't  be diagonalizable.  For what I got this matrix is diagonalizable for every $b$ value.  Please write me also the final answer, thank you very much. How may I reference the script tag that loaded the currently-executing script? How widespread is the practice of delegating LoR writing to the applicant? At least two questions (, ) on this site indicate that in more than a few isolated cases at least, letters of recommendation are in fact written by the applicant and only signed off (or perhaps rephrased somewhat) by the recommender, who would actually be responsible for writing the letter.  Is there any evidence about the prevalence of this practice that goes beyond anecdotes? I realize that cross-country (cultural) difference may play a role. combinatorics circular arrangement problem If $n$ distinct things are arranged in a circle, then what are the number of ways selecting three of these things so that no two of them are next to each other? What is the rule for omitting/including the definite article in the following sentences:     I used to play piano.   I used to play the piano.   I would pick the first sentence, but I've heard people say the second sentence even when they are not referring to a specific piano. Which one is correct? Book covering differential geometry and topology for physics I'm interested in learning how to use geometry and topology in physics. Could anyone recommend a book that covers these topics, preferably with some proofs, physical applications, and emphasis on geometrical intuition? I've taken an introductory course in real analysis but no other higher math.