Why given function is not exact?
Prove that ${x dy - y d x\over x^2 + y^2}$ is not exact
Today I saw a sentence:  She surely can do it.  What does that mean? How does it differ from:  She certainly can do it. Surely she can do it.  This slight difference in meaning of those sentences I am not able to notice. Could you please help me? Thanks in advance! I remember reading this as a kid and it starts out with:   a boy in his home village where the other kids are mean to him during sports and they heat up their home with floating logs or something.   The kid is being hunted by some reaper character and that reaper finds him at a place called "The Edge" or something similar.   He buys a glove covered in an expensive dust that purifies things and is really rare.  In one book they had to climb down the edge for some reason.  There was another part where people only communicated telepathically and when sneaking into somewhere he only thought of light.  One of the main things is the floating ships and how he is really good at flying them and he assembles a team for a mission or something.  There is like float powder and stuff.  I read this close to 10 years ago. What EXACTLY cause Voldemort's soul piece to split off when he killed Lily and tried to kill Harry? Cardinality of a totally ordered union Let $(X_{\alpha})_{\alpha \in A}, (Y_{\alpha})_{\alpha \in A}$ be families of sets such that for $\{X_{\alpha} \mid \alpha \in A \}$ and $\{Y_{\alpha} \mid \alpha \in A \}$ are totally ordered by inclusion. We have $(X_{\alpha},Y_{\alpha}) \neq (X_{\beta},Y_{\beta})$ for $\alpha \neq \beta$. Suppose that $|X_{\alpha}| \leq |Y_{\alpha}|$ for any $\alpha \in A$. It is true that $|\bigcup_{\alpha} X_{\alpha}| \leq |\bigcup_{\alpha} Y_{\alpha}|$? How to copy all files of a certain type into a folder from command prompt? I want to copy all files of a certain type (like .docx, .pdf, etc) on my PC into a folder. How can I do that? When should I use "a" versus "an" in front of a word beginning with the letter h? A basic grammar rule is to use an instead of a before a vowel sound. Given that historic is not pronounced with a silent h, I use “a historic”. Is this correct? What about heroic? Should be “It was a heroic act” or “It was an heroic act”?  I remember reading somewhere that the h is sometimes silent, in which case it’s an, and when the h is pronounced, it’s a. But then I also remember reading that it depends on which syllable is stressed. And I also think I read somewhere that it might differ between British and American English.  Personally, I pronounce the h, and believe that a is correct. I find that it sounds incorrect to use an and pronounce heroic without the h.  So how do I know when to use a and when to use an with a word beginning with the letter h? Are both acceptable or is there one that is correct? Let $P,Q$ real $n\times n$ matrices  such that $P^2=P$ , $Q^2=Q$ and $I-P-Q$ is an invertible matrix.  Prove that $P$ and $Q$ have the same rank.  Some help with this please , happy year and thanks. Question 1: Why are irrational numbers uncountable and rationals countable?  I really struggle to understand this. I initially thought it had something to with the fact that between any two numbers there will always be a irrational number. But now it has come to my attention that the same holds for rational numbers. So I can't really see the difference between them. What is it that makes the difference? Why can we line up all rational numbers one-to-one with the natural numbers, but not the irrationals with the naturals?  Sorry for a perhaps basic question, but I really, really struggle with it. Thanks. Cardinality of Borel sigma algebra Let $R$ be an rng. (There may be no unity)  Then, does there always exist a ring(with unity) $A$ such that $R$ is a subrng of $A$? When is R squared negative? My understanding is that $R^2$ cannot be negative as it is the square of R. However I ran a simple linear regression in SPSS with a single independent variable and a dependent variable. My SPSS output give me a negative value for $R^2$. If I was to calculate this by hand from R then $R^2$ would be  positive. What has SPSS done to calculate this as negative?   R=-.395 R squared =-.156 B (un-standardized)=-1261.611   Code I've used:  DATASET ACTIVATE DataSet1.  REGRESSION /MISSING LISTWISE /STATISTICS COEFF OUTS R ANOVA             /CRITERIA=PIN(.05) POUT(.10) /NOORIGIN             /DEPENDENT valueP /METHOD=ENTER ageP   I get a negative value. Can anyone explain what this means? Why is current a scalar quantity? Tweak showlabels/showkeys - wrap the label Can showlabels wrap the label in the margin? A very similar question is , but the solution of @DavidCarlisle does not solve the more general case. Consider the following MWE:  \documentclass{article} \begin{document} \begin{figure}[ht]   \centering   \rule{1cm}{1cm}   \caption{default}   \label{fig:a very very very long and detailed label} \end{figure} \end{document}   When adding the package showkeys the output is:    Similar problem occurs with the showlabels package (whether the hack of @DavidCarlisle is used or not):   So, is there a way to fix it? Can't start ubuntu-desktop after upgrade to 18.04 After the restart step of upgrading Ubuntu to 18.04, tty is opening instead ubuntu-desktop. And when I enter my login name and password, I am still in the tty. This is happening again in every restart. How can I start the graphical desktop as normal? How to turn the white colour portion to transparent I got this map icon in work in illustrator, and would like to turn those white dash line and the white outline of the location mark to transparent. Can you please advise me how to do it? Thank you in advance. Is there animation software available? Is there commercial-grade computer animation software available for Ubuntu, similar to the professional software sold for the Windows operating system?  This question goes out to those of you who may be using such software professionally.  My daughter recently graduated from the Art Institute of Seattle, and needs to put together an animation portfolio in order to interest employers in the field.  As you know, such software is usually provided by the employer and the costs are high - several thousand dollars.  I suggested that she investigate Ubuntu as a possible way to acquire the tools she needs.  But, since I have no idea what might be available, either as open source or proprietary animation software, I am reaching out to the Ubuntu community for help in the hope someone who is using such software can help her.  Thank you for reading this post, and for any information you might have. Is there a word for happiness made possible by a tragic situation? I'm new to tikz-qtree, and can't find an automatic way to do something that qtree did very nicely.  With qtree, if you don't have a label for a single intermediate node, you get a straight line from the grandmother to the granddaughter.  With tikz-qtree, you get a "kink".  Compare the following:  With qtree:  \documentclass{article} \usepackage{qtree}  \begin{document}  \Tree [ Wiiiiiiiiiide [ nar- -row ] ]  \Tree [ nrw [ wiiiiiiiiiiiii- -iiiiiiiiiiiide ] ]  \end{document}   With tikz-qtree  \documentclass{article} \usepackage{tikz,tikz-qtree}  \begin{document}  \Tree [ Wiiiiiiiiiide [ nar- -row ] ]  \Tree [ nrw [ wiiiiiiiiiiiii- -iiiiiiiiiiiide ] ]  \end{document}   Is there any way to get the nice straight line in tikz-qtree, or do I have to adjust it manually?  Thanks in advance. A potentially dangerous Request.Form value was detected from the client Every time a user posts something containing &lt; or &gt; in a page in my web application, I get this exception thrown.  I don't want to go into the discussion about the smartness of throwing an exception or crashing an entire web application because somebody entered a character in a text box, but I am looking for an elegant way to handle this.  Trapping the exception and showing     An error has occurred please go back and re-type your entire form again, but this time please do not use &lt;   doesn't seem professional enough to me.  Disabling post validation (validateRequest="false") will definitely avoid this error, but it will leave the page vulnerable to a number of attacks.  Ideally: When a post back occurs containing HTML restricted characters, that posted value in the Form collection will be automatically HTML encoded. So the .Text property of my text-box will be something &amp; lt; html &amp; gt;  Is there a way I can do this from a handler? In our 5e game, we stole a boat. And a horse carriage. And a lot of other stuff for moving things between cities.   Our DM meant for this to be a way to skip road encounters. We decided to fund a shipping company and hire managers (Knights retainers, etc.) to turn a profit. The DM ruled that these would cover lifestyle expenses, provide us with easy smuggling, etc.   However, we want to keep tabs on the treasure we're moving back and forth.   What can we use for communicating with our managers from anywhere in the world? What about from say, across the city?  We don't need to communicate often or for long - a single round will work. All we need is for the manager to say "we need you back"