How do I rotate a group of vertices without deforming its shape?
Aligning Vertices Diagonally
Java method dispatch with null argument I have heard several pseudoscientific explanations about the  and find them hard to believe.  As a mathematician mainly focusing on functional analysis, I have a considerable interest in this matter. Although I still have no idea about it, I aim to truly understand it one day. For now, the question is:  Can the Heisenberg Uncertainty Principle be explained so that a non-scientist can at least get a correct idea of what it says and what not?  One of the most heard explanations is the one that says naïvely that while trying to determine the position of a particle you send energy (light) so you modify its speed, therefore making it impossible to determine the speed. If I understand well this should only be a some sort of metaphor to explain it, right? What immigration and customs checks are performed for passengers leaving the U.S.? What does The Doctor's Speech in The Rings of Akhaten refer to? I recently watched the brilliant speech from The Rings of Akhaten again. For those who haven't seen it or don't remember it:     I walked away from the last Great Time War. I marked the passing of   the Time Lords. I saw the birth of the universe and I watched as time   ran out, moment by moment, until nothing remained. No time. No space.   Just me. I walked in universes where the laws of physics were devised   by the mind of a mad man. I've watched universes freeze and creations   burn. I've seen things you wouldn't believe. I have lost things you   will never understand. And I know things. Secrets that must never be   told. Knowledge that must never be spoken. Knowledge that will make   parasite gods blaze. So come on, then. Take it! Take it all, baby!   Have it! You have it all!   Some of these I understand:     I walked away from the last Great Time War.    Clear enough     I marked the passing of the Time Lords.   Again makes sense, given he "killed" them.     I saw the birth of the universe and I watched as time ran out, moment by moment, until nothing remained. No time. No space. Just me. I walked in universes where the laws of physics were devised by the mind of a mad man. I've watched universes freeze and creations burn.   I'm very vague on this put is some of it related to The Big Bang?     I've seen things you wouldn't believe. I have lost things you will never understand. And I know things. Secrets that must never be told. Knowledge that must never be spoken. Knowledge that will make parasite gods blaze.   Possibly relating to the question which must never be answered, but at this point we've not been to Trenzalore so does he even know what knowledge is and why?  What do the unknown sections of these speech refer to? In general, what is meant by saying that the fraction $x$ of the variance in an analysis like PCA is explained by the first principal component? Can someone explain this intuitively but also give a precise mathematical definition of what "variance explained" means in terms of principal component analysis (PCA)?  For simple linear regression, the r-squared of best fit line is always described as the proportion of the variance explained, but I am not sure what to make of that either. Is proportion of variance here just the extend of deviation of points from the best fit line? Boats from Manaus, Brazil to Leticia, Colombia? I've heard of and met a few people who have done this route, and I hope to do it at the end of this year or early next year.  However, the descriptions were mostly sketchy, and I'm wondering if it's a regularly scheduled service, or more ad-hoc.  So I guess the question is, how can I find out which boats go from Manaus to Leticia, and when they go?  Ideally this wouldn't be a tour, but a 'locals' boat. I would like to transfer files between two remote hosts using on local shell, but it seems rsync doesn't support synchronisation if two remotes are specified as follow:  $ rsync -vuar host1:/var/www host2:/var/www The source and destination cannot both be remote.   What other workarounds/commands I could use to achieve similar results? How to get WordPress' hooks/actions run sequence? In what order add_action hooks execute? i.e. init wp_head wp_footer after_theme_setup  etc... ??? ??? ???     EDIT: I've also posted my solution. I know it existed as sort of a folder in Windows Explorer in at least Windows XP, but I just can't seem to find it in Windows 7...  How can I take a picture with my webcam in Windows 7 without using any 3rd party tools? When do I use active vs passive perception? So, I'm trying to figure out how to run the scene from the beginning of Lost Mine of Phandelver (5e starter set) where the party is ambushed by goblins and I'm really confused as to how Passive Wisdom (Perception) works.  The included rulebook mentions on page 6 :     When you hide, there’s a chance someone will notice you even if they aren’t searching. To determine whether such a creature notices you, the DM compares your Dexterity (Stealth) check with that creature’s passive Wisdom (Perception) score, which equals 10 + the creature’s Wisdom modifier, as well as any other bonuses or penalties. If the creature has advantage, add 5. For disadvantage, subtract 5. For example, if a 1st-level character (with a proficiency bonus of +2) has a Wisdom of 15 (a +2 modifier) and proficiency in Perception, he or she has a passive Wisdom (Perception) of 14.   So the party is being ambushed by goblins and at that point the DM guide mentions on page 7 :     Check to see who, if anyone, is surprised. [...] Make a Dexterity (Stealth) check for the goblins, rolling once for all of them. Roll a d20, add the goblins' Stealth skill modifier (+6) to the roll and compare the result to the characters' Passive Wisdom (Perception) scores.   So to me this reads like I should roll 1d20+6 for the goblins and compare that to the static Passive Wisdom (Perception) score on the character sheet of a PC. The PCs don't get to roll anything as they're not actively looking for enemies, even though they are investigating the dead horses.  I would also think that if the characters were supposed to roll, the DM guide would clearly instruct so, given that this is the starter set.  However, watching  at around 8:01 I notice that the DM is explicitly asking his party for a perception roll. And the same thing happens on a couple of other videos where people are running the Lost Mine adventure. The DM always requests a roll.  So what gives? Shall I take it that the DMs ask for the roll because they consider the party to be actively seeking for hidden foes? Or am I just misreading the rulebook and the DM guide? Given $f = f(u(t), t)$, is it possible to find the following derivative? ($f$,$u \in \mathbb{R}^n$, $t \in \mathbb{R}$)  $$ \frac{\partial f}{\partial||u||^2_2} $$  I am aware of the following derivatives:  $$ \frac{\partial||x||^2_2}{\partial x} = \frac{\partial ||x^Tx||_2}{\partial x} = 2x $$  So I can invert it to give me (elementwise division in the RHS)  $$ \frac{\partial x}{\partial||x||^2_2} = \frac{1}{2x} $$  This step does feel like abuse of notation I find it hard to convince myself of its validity.  If it's right though, I could just apply the chain rule to find  $$ \frac{\partial f}{\partial u} \frac{\partial u}{\partial||u||^2_2} $$  However, knowing that both $f$ and $u$ are a function of $t$, I am somehow doubting my own reasoning. Or does that just mean that the derivative will still be a function of $t$ and I have nothing to worry about? Can anyone shed some light?  UPDATE: I'm now doubting the existence of  $$ \frac{\partial u}{\partial ||u||^2_2} $$  because $u = u(||u||_2^2)$ is not injective. Is the inversion step I did above legitimate? Is there another possible approach? Strange characters when the output of `ls` is redirected to a file I want to list the components of the current working directory in a text file  ls -1 &gt; textfile   Output looks fine with more.   1010661085645 1010729039145 1010747080245 1010849051345 1010859053445 1011046075845   However when I view this textfile with emacs, several strange characters appear  [0m[01;34m1010661085645[0m [01;34m1010729039145[0m [01;34m1010747080245[0m [01;34m1010849051345[0m [01;34m1010859053445[0m [01;34m1011046075845[0m   Can anyone explain what is going on here? Why did Sirius Black's family live among Muggles? Anomalous community user activity On the meta home page I noticed the  is listed as doing something, but cannot figure out what it is.  There is nothing on the  or its , but the recent activity is listed with the same timestamp. SQL Server Dependencies Is there an easy way to chase down table/stored procedure/function dependencies in SQL Server 2005+?  I've inherited a giant application with lots of tables and even more stored procedures and functions that are long and interlinked.    At the end of the day is there a way to build a dependency tree?  Ideally what I'm looking for goes in both directions:  For a table/procedure - what depends ON it?:  Show me all the stored procedures that eventually reference it (ideally in a tree view such that sub procedures nest out to the bigger procedures that call them)  For a procedure - what does IT depend on?:  Show me all the procedures and tables that a given procedure will (or could) touch when running.  It seems this tool shouldn't be that hard to make and would be incredibly useful for DB maintenance generally.  Is anyone aware of such a thing?  If this doesn't exist, why the heck not?  The built-in functionality in Management Studio is nice but the information does not appear to be complete at all. How do I evaluate these fork() calls with the && and || operators in C? So I have this word problem and I’m a bit confused about it. I have the answer and explanation but I still don’t understand: The half-life of carbon-14 is approximately 5730 years, while the half-life of carbon-12 is essentially infinite. If the ratio of carbon-14 to carbon-12 in a certain sample is 25% less than the normal ratio in nature, how old is the sample?     A. Less than 5730 years      B. Approximately 5730 years      C. Significantly greater than 5730 years, but less than 11460 years      D. Approximately 11460 years  Correct Answer: A Explanation: Because the half-life of carbon-12 is essentially infinite, a 25 percent decrease in the ratio of carbon-14 to carbon-12 means the same as a 25 percent decrease in the amount of carbon-14. If less than half of the carbon-14 has deteriorated, then less than one half-life has elapsed. Therefore, the sample is less than 5730 years old. Be careful with the wording here—the question states that the ratio is 25% less than the ratio in nature, not 25% of the ratio in nature, which would correspond to choice (D). How is the ratio of the carbon isotopes relevant to half-lives? What is the purpose of saying the half-life of an isotope is infinite? What is meant by “the normal ratio in nature”? Just based on the answer, it seems like the question said “25% of a carbon sample decayed, how old is this sample?” Obviously it’s younger than 5,730 years (the time for its first half life) because if only 25% decayed that means half a half-life has passed. I don’t see how isotopes and ratios would change this problem at all. Edit: Every answer here was very informative and helpful. It was tough to pick a best answer. I picked Cosma’s because it clicked with me. If you’re reading this and want to understand radiocarbon dating, look at every answer because there is some useful information in every answer I am going to start a phd at the US with an F1 visa. University told me that I could enter the US only 30 days before the date on I-20. Since English is not my first language (and this would be a big change in my life) I would like to go there by June.  The thing is that I have an European passport with a valid ESTA. My plan would be to arrive with this passport, stay 4-6 weeks , go to Canada for a short vacation (maybe flight maybe by land) and come back to the USA with F1 visa.  I have two questions about this:  1) is this possible?   2) If yes, how could I justify knowing I will lose my come-back flight during my first entry? (I would purchase round trip because one-way are too expensive, probably with less than 90 days difference) 3D software like GeoGebra Does it exist a free interactive geometry software, like GeoGebra, which works for 3D geometry? I would be able to draw spheres, great circles, and so on. To tell about a guess about a case in the past, why use "would+have+past participle" instead of "must+have+past participle? I have seen this sentence in an article on bbc, which is about how people lived thousands of years ago. &quot;When this Neolithic home was built, it would have had a cosy roof of turf..&quot; When I read it, I got confused. Because the fact seems as a simple past situation or guessing/assumption about something in the past. it simply gives information about a past event, eg &quot;when I was a child, I had a blue toy car. I have been making a lot of research on whether or not this structure &quot;would+have+past participle&quot; could be used instead of the simple past or &quot;must+have+past participle&quot;, but I could not find any satisfying explanation. Almost all grammer contents cover this structure is used when we imagine the opposite of what actually happened in the past eg. &quot;referring to a missed opportunity&quot; (eg. &quot;if you had come to the party, you would have seen Tom.&quot;), But, in this case of this sentence, &quot;type 3 conditional&quot; is irrelevant. It is not an if sentence,  It simply gives information about how this house was like or was probably like when it was built long ago. Just like it would be If and old lady would want to tell about &quot;how she was like when she was a child years ago. she would simply say &quot;when I was a child, I had long curly hair.**. So &quot;when I was a child, I would have had long curly hair.&quot; would be wrong. So, my question is: 1-Does this structure &quot;would+have+past participle&quot; completely replace simple past sentences? or can be it be used instead of simple past? 2- If this structure was simply used because the author was not %100 sure about the fact as it was a long long time ago -so he wanted to make a guess or assumption, why did he not simply use &quot;must+have+past participle&quot; or &quot;it was likely that blah blah&quot; which must be used for guessing or assumptions about past happenings. Would it not have made more sense if it was like: &quot;When this Neolithic home was built, it must have had a cosy roof of turf.