subject verb agreement: "the downside are the messages" Which is the correct one:     the big downside is the imperfect messages the user gets.        the big downside are the imperfect messages the user gets.   I am almost sure the second one is correct with "the messages" being the subject and "are the downside" the predicative nominal.
Agreement in "[Singular Noun] Is/Are [Plural Noun]"? My fish's native habitat is rice fields. My fish's native habitat are rice fields.   Which one is correct? I'm pretty sure it's the first, since 'is' modifies 'habitat,' but it still sounds weird...
I have a PCB with documentation. In the documentation, there is referred to specific pins of several jumpers and connectors. On the PCB however, there isn't a label or so for which pin has what number. I need to figure out which pin has which number, so that I know the function of each physical pin.  I noticed all connectors have all pins with a rounded tin pad, whilst one pin (either the first or the last when counting from right to left) has a square tin pad:     Is it some kind of convention which number this pin has? After that, how to count the other pins? Differences between astronomy, astrophysics and cosmology? I want to add a check constraint on a column if entered value for column is greater than 3 than it should be saved as 1 else entered value. For that scenario I am using below query but on insertion of data it shows an error message.  create table tblTestCheckConstraint  ( id int, NewColumn int )   alter table tblTestCheckConstraint add constraint chk_tblTestCheckConstraint_NewColumn1 CHECK   (     CASE         WHEN NewColumn &gt;4 THEN 1         ELSE NewColumn     END = 1 )   Insert Statement:   insert into tblTestCheckConstraint values ( 1,5) insert into tblTestCheckConstraint values ( 1,2)   Error Message:   Msg 547, Level 16, State 0, Line 1 The INSERT statement conflicted with the CHECK constraint "chk_tblTestCheckConstraint_NewColumn1". The conflict occurred in database "DBName" , table "dbo.tblTestCheckConstraint", column 'NewColumn'. The statement has been terminated. Can the team provide some explanation for declined feature requests? Could the team try to leave at least a little explanation when tagging a feature-request post with the "status-declined" tag?  On Uservoice there was usually a brief explanation.  I'm not saying it should be mandatory or anything, it would just be nice. Calculating proportional area of polygon within another layer's polygon using QGIS? How to setup Windows from an external hard drive? Is it possible to install Windows from an external hard drive?  I have Windows XP installed on my laptop, and I want to remove it and install Windows 7.  My Windows 7 installation is in an .iso format on an external USB hard drive.  Is it possible to install it or will I need to put in a DVD before I start installing? Lots of questions in the reopen queue I've noticed in the last couple of days that there have been a few occasions when there's been a sudden surge of questions in the SO "Reopen" review queue.  Normally there's either no questions at all to reopen or at most three or four, and that's still the case, except that for the last couple of days I've gone to the review page and seen about fifty-odd questions in the queue, where just moments before there had been none.  I've gone through the reviews and the questions themselves seem reasonably legitimate (including the occasional audit), so I'm not questioning that... it just seems odd that there would be so many more than usual all of a sudden, and that they'd all appear at once.  Anyone got any insights, or should I just chalk this down as "one of those things"? Reputation misaligned in new topbar How can you use optional parameters in C#? Note: This question was asked at a time when C# did not yet support optional parameters (i.e. before C# 4).  We're building a web API that's programmatically generated from a C# class. The class has method GetFooBar(int a, int b) and the API has a method GetFooBar taking query params like &amp;a=foo &amp;b=bar.   The classes needs to support optional parameters, which isn't supported in C# the language. What's the best approach? Field level permissions in Drupal 7 What is the best way to create a piece of content with multiple fields... allowing users to edit the content as a whole yet blocking the ability to edit.  The setup I have is a piece of content that has 3 fields: Body, PDF, SWF... and a "Selector" (List Text) that's tied via dependancy. So the user chooses BODY, PDF or SWF and that's what available to edit and shown on the page when live.  What I want to do is add a PHP field... that's either:     greyed out (unable to edit) if your not admin...   doesn't show up in the Drop Down list... Can't select it if you can't see it Shows up on the drop down, but the field doesn't show up in the editor without permissions.   I hope I'm making sense... I can provide an example if needed. I have bought return tickets from London to Lille Europe on Eurostar. The trains on my outward and inbound journeys both stop at Calais Frethun.  Will Eurostar let me get on in Calais on the inbound? What about getting off at Calais on the outbound leg? I suspect leaving the train early is easier than getting on the train 'late'. Circle-Rectangle collision detection (intersection) How can I tell whether a circle and a rectangle intersect in 2D Euclidean space? (i.e. classic 2D geometry) Area of a quadrilateral proof GeoReference tiff image into the Google map? I want to Geo-reference a tiff image contain a Map for a specific region, I need to add this region(image) and Geo-reference it on the Google map, SO I can see on the map for the region I select the image which I have inserted.  the image also need information such as the Latitude and Longitude of corners and size, and the pixel per meter measurement.  How to do the correct Geo-reference for that ? I'm doing some exercises on Apostol's calculus, on the floor function. Now, he doesn't give an explicit definition of $[x]$, so I'm going with this one:     DEFINITION Given  $x\in \Bbb R$, the integer part of $x$ is the unique $z\in \Bbb Z$ such that $$z\leq x &lt; z+1$$ and we denote it by $[x]$.   Now he asks to prove some basic things about it, such as: if $n\in \Bbb Z$, then $[x+n]=[x]+n$  So I proved it like this: Let $z=[x+n]$ and $z'=[x]$. Then we have that  $$z\leq x+n&lt;z+1$$  $$z'\leq x&lt;z'+1$$  Then $$z'+n\leq x+n&lt;z'+n+1$$  But since $z'$ is an integer, so is $z'+n$. Since $z$ is unique, it must be that $z'+n=z$.  However, this doesn't seem to get me anywhere to prove that  $$\left[ {2x} \right] = \left[ x \right] + \left[ {x + \frac{1}{2}} \right]$$  in and in general that   $$\left[ {nx} \right] = \sum\limits_{k = 0}^{n - 1} {\left[ {x + \frac{k}{n}} \right]} $$  Obviously one could do an informal proof thinking about "the carries", but that's not the idea, let alone how tedious it would be. Maybe there is some easier or clearer characterization of $[x]$ in terms of $x$ to work this out.  Another property is $$[-x]=\begin{cases}-[x]\text{ ; if }x\in \Bbb Z \cr-[x]-1 \text{ ; otherwise}\end{cases}$$  I argue: if $x\in\Bbb Z$, it is clear $[x]=x$. Then $-[x]=-x$, and $-[x]\in \Bbb Z$ so $[-[x]]=-[x]=[-x]$. For the other, I guess one could say:  $$n \leqslant x &lt; n + 1 \Rightarrow  - n - 1 &lt; x \leqslant -n$$  and since $x$ is not an integer, this should be the same as $$ - n - 1 \leqslant -x &lt; -n$$  $$ - n - 1 \leqslant -x &lt; (-n-1)+1$$  So $[-x]=-[x]-1$ Movie with killer androids (glowing eyes, screaming) Copyright issues if using vector art from Shutterstock? Why does an overridden function in the derived class hide other overloads of the base class? I was solving a few problems from a textbook and I came across this one:     Find the tangent lines to the graph of $x^2+4y^2 = 36$ that go through   the point $P=(12,3)$   I could find the tangency points $$ but my solution was completely messy (I had four equations that I had to go back-and-forth with.  Is there an elegant/simple solution to that?  Tangency points:  $$P_1 = (0,3)$$ $$P_2 = \left( \frac{24}{5} , 3-\frac{24}{5} \right)$$ How to place a float at the top of a floats-only page? I just got a short algorithm on my page, and it keeps getting aligned at the center of the page. But I want to have it aligned at the top, what do I have to do?