Which anchors to use for a wall in a basement
How do you secure wood framing to a concrete basement floor?
Show that unit circle is not homeomorphic to the real line What is Quantization? Why does stdafx.h work the way it does? As usual, when my brain's messing with something I can't figure out myself, I come to you guys for help :)  This time I've been wondering why stdafx.h works the way it does? To my understanding it does 2 things:   Includes standard headers which we might (?) use and which are rarely changed Work as a compiler-bookmark for when code is no longer precompiled.   Now, these 2 things seems like two very different tasks to me, and I wonder why they didn't do two seperate steps to take care of them? To me it seems reasonable to have a #pragma-command do the bookmarking stuff and to optionally have a header-file a long the lines of windows.h to do the including of often-used headers... Which brings me to my next point: Why are we forced to include often-used headers through stdafx.h? Personally, I'm not aware of any often used headers I use that I'm not already doing my own includes for - but maybe these headers are necessary for .dll generation?  Thx in advance How accurate is approximating the Earth as a sphere? What level of error do I encounter when approximating the earth as a sphere? Specifically, when dealing with the location of points and, for example, the great circle distances between them.  Are there any studies on the average and worst case error compared to an ellipsoid? I'm wondering how much accuracy I'd be sacrificing if I go with a sphere for the sake of easier calculations.  My particular scenario involves directly mapping WGS84 coordinates as if they were coordinates on a perfect sphere (with the  defined by the IUGG) without any transformation. Suppose the terms of the sequence of real numbers $\{a_n\}$ satisfy $|a_{n+1} - a_n| \le 2^{-n}$ for all $n$. Prove that $\{a_n\}$ is Cauchy.   My Work  So by the definition of a Cauchy sequence, for all $\varepsilon &gt; 0$ $\exists N$ so that for $n,m \ge N$ we have $|a_m - a_n| \le \varepsilon$. However, questions like  make me understand that the $2^{-n}$ condition is necessary for this to be a true statement.   So I am wondering how to appeal to the Cauchy definition for this proof. Do I prove that every convergent sequence is therefore Cauchy, and then try to prove convergence? How can friction do no work in case of pure rolling? Let $\mathbb{F}$ be a finite field.  Let $a_1,\dots,a_n \in \mathbb{F}$ be given.  I want to know whether there exists $x_1,\dots,x_n \in \mathbb{F}$ such that  $$a_1 x_1^2 + a_2 x_2^2 + \dots + a_n x_n^2 = 1.$$  My question: Can we characterize when this equation has a solution, i.e., by some criterion on $a_1,\dots,a_n$?  Is there a clean characterization, in terms of $a_1,\dots,a_n$ and the properties of $\mathbb{F}$?    Here's what I can see immediately.  First, if $n=1$, there is an easy answer (the equation has a solution iff $a_1$ is a square in $\mathbb{F}$).  Second, if any $a_i$ is a square in $\mathbb{F}$, the equation has a solution (set all other $x_j$'s to $0$), so we can assume that all the $a_i$'s are non-squares and that $n \ge 2$.  Third, if $-1$ is a square in $\mathbb{F}$, then the equation has a solution: we can take $x_2 =  \sqrt{-a_1/a_2} \cdot x_1$.  But what about the case where $-1$ is a non-square in $\mathbb{F}$?  Is it always guaranteed to have a solution in this case? Proof that every repeating decimal is rational When do moderator elections take place? I'm really confused on this. I have no idea on several things:   When do elections begin?   Is there a set time each year?   Do elections actually take place each year?   Can I vote?   Where do I vote?     Etc.  Can someone please help me? Using a new document class/template with LyX? I tried googling this elsewhere but I'm new to LaTeX and extremely confused about certain things. Basically I downloaded MikteX and I'm using the latest version of Lyx with it. Now all I basically know how to do is make pretty looking mathematics and add contents pages/titles/references/etc.  I'm looking to make a dissertation and my unviersity provides a template,  (available for download at that link).  So, what exactly do I need to do (and please be super specific as I am totally clueless to all the jargon I read).   Basically, I need to download ociamthesis.cls in the first line of that webpage. Does it matter where I save it? What exactly do I do next? How do I fix my locale issue? I am getting this message every time I do something like starting or stopping a service.  perl: warning: Setting locale failed.    perl: warning: Please check that your locale settings:            LANGUAGE = "en_US:en",            LC_ALL = (unset),            LC_MESSAGES = "en_US.UTF-8",            LANG = "en_US.UTF-8"        are supported and installed on your system.    perl: warning: Falling back to the standard locale ("C").    locale: Cannot set LC_CTYPE to default locale: No such file or directory    locale: Cannot set LC_MESSAGES to default locale: No such file or directory    locale: Cannot set LC_ALL to default locale: No such file or directory    (Reading database ... 21173 files and directories currently installed.)   Removing bind9 ...    * Stopping domain name service... bind9                                        [ OK ] Processing triggers for man-db ...    locale: Cannot set LC_CTYPE to default locale: No such file or directory    locale: Cannot set LC_MESSAGES to default locale: No such file or directory    locale: Cannot set LC_ALL to default locale: No such file or directory      How do I fix this error ? Short-lived sci-fi series with a former astronaut turned superhero (or maybe a police officer?) using his spacesuit for his "powers" Plot Details/Summary I only watched an episode or two of this one, so I can't recall a whole lot about it.  The protagonist is a former astronaut of some sort, who makes it his mission to clean up the crime in his city.  He might have been a police officer in his &quot;new life&quot; or he might have decided to become a sort of quasi-superhero.  In either case, I distinctly recall his space suit being the gimmick that makes him an effective crime fighter in the show.  I seem to recall the protagonist being a young, dark-haired man, and I think he had a friendship or an alliance with a young woman (maybe a fellow cop, or someone from the space program?).  I don't think there were alien beings in the show.   The criminal threats were all quite terrestrial, IIRC. Timeframe and other Publication Details This was a syndicated tv show I saw on American television, probably around the late 90s to early 2000's.  I believe the show was filmed in Canada, though I'm not certain.  I don't think it lasted very long - it was pretty dreadful.  I can say for certain the show is not Space Cop or Gerry Anderson's Space Precinct. Obscure fantasy movie involving flying sea-galleons and a time weapon Been trawling the internet for hours, can't find any trace or reference of this movie. Not really sure what station I saw it on (only once), but it was probably Sci-Fi Channel (mind you, a very long time ago:  Movie opens with flying ships (sailing galleons), that proceed to siege a towering city. The city fires back with its own cannons, and drives the invaders away. The main protagonist is a young boy who longs to be a knight... or this movie's equivalent thereof. He has an older brother who is already recognized as a warrior. The boy lives in the city that successfully repelled this siege.  The king of this city has some sort of wizard or wise-man as a councilor, who conceives an "ultimate weapon" against their enemies- an hourglass of sorts that accelerates time against a target. However, during the course of the movie this weapon is stolen by the city's enemies (led by an evil queen or sorceress), who proceeds to use it against the city itself and all its inhabitants.  So the king sends out his armies to retrieve the artifact, all the while everyone and everything begins aging rapidly. Our boy-hero watches his older brother (now much older) set out with other knights on the quest, and there's a token romance between the boy and the king's daughter. The knights do not return, however, and the time-curse continues to wreak havoc on the city.  Ultimately, the boy (now a man) sets out to find his brother, the hourglass, and save the day. He finds his brother at a wreckage-site (I believe of a flying galleon), and they share a brief moment before the elder brother finally succumbs to old age. I'm sure I'm forgetting some other poignant details, but that's essentially the crux of it. Ends... if I remember correctly, with  the artifact being disabled and the evil queen/sorceress defeated.  Question is: what is this movie titled? How do I restore the default repositories? Should I use an offset for my Poisson GLM? I am carrying out research to look at differences in fish density and fish species richness when using two different underwater visual census methods. My data was originally count data but then typically this is changed to fish density but I have still decided to use a Poisson GLM, which I hope is right.   model1 &lt;- glm(g_den ~ method + site + depth, poisson)   My 3 predictor variables are method, site and depth which I ordered as factors when I input them.   My response variables are grouper species richness, grouper density and the same for other fish groups. I am aware that density is not an integer and it is numerical data e.g 1.34849. I am now however getting this error:      In dpois(y, mu, log = TRUE) : non-integer x = 0.037500   I've been reading up and many people suggest using an offset, is this the most advisable thing to do? Prove the divergence of the sequence $\left\{ \sin(n) \right\}_{n=1}^{\infty}$. I am looking for nice ways of proving the divergence of the sequence $\left\{x_n\right\}_{n=1}^{\infty}$ defined by $$x_n=\sin{(n)}.$$ One (not so nice) way is to construct two subsequences: one where the indexes are picked such that they lie in the intervals  $$I_k=\left(\dfrac{\pi}{6}+2\pi(k-1),\dfrac{5\pi}{6}+2\pi(k-1)\right)$$ and one where they lie in $$J_k=\left(\dfrac{7\pi}{6}+2\pi(k-1),\dfrac{11\pi}{6}+2\pi(k-1)\right).$$ If ${x_n}$ converges, then all its subsequences must converge to the same limit, but here the first subsequence has all its values in the interval $\left[ \frac{1}{2}, 1\right]$ while the second has its values in $\left[-1,-\frac{1}{2}\right]$. Contradiction.  Filling the details of this proof is rather tedious and not very elegant. Anyone has a better idea? Given the following image:   $\hskip{1.5 in}$   Supposing $A(100, 300)$ and $B(300, 100)$, how can I find the angle $\alpha$ between A and B?  On a side note, what's the main difference between a point and a vector? translating a point to a vector is as simple as Point = Vector? Sometimes I find articles where the terms are interchangable Why do Kurama and Gyuki appear as chakra while other bijuu don't? In Naruto, Kurama (the Nine-tailed bijuu) appears as chakra, as does Killer B's bijuu, Gyuki.      Other bijuu, however, don't appear that way. What is different between them? Why does everyone do 9-overlord, not 10-overlord? Safety of installing Ubuntu alongside Windows Is it really safe to choose the "Install Ubuntu alongside Windows" option from the Ubuntu installation program?  I never used that option, instead I used other tools such as partition magic or windows 7's disk tool to resize my partitions.  Since I'm going to install Ubuntu across a lot windows (XP, Vista and 7) machines. It would not be nice to damage those Windows partitions.  What is your experience? Can I use this feature without concerns?