What’s the farthest I could travel back in time and converse properly in English?  And what caused this ‘new style’ of English speaking [that we know (and love) today]?
I have seen several times on TV documentaries where the presenter is taken to something like a library archive, and shown a book which they proceed to read an excerpt from.  On a couple of occasions the camera has shown the text they were reading and generally I have thought that I would struggle to read the words because of how the letters were formed (e.g. , or ).  This got me to wondering about how pronunciation and sentence formation may have changed over time as well, and how far back in time could I travel and still be understood while speaking my "modern" English in England (while obviously not talking about modern concepts like mobile phones or space travel)?
Integral $\int\frac{dy}{(y^2 + ay + b)^{3/2}}$ Need the indefinite integral with $a,b$ constants. This is not a homework question. Need it for a physics problem. About big parenthesis larger than Bigg case insensitive find in mongodb for usernames in php Give the "some of your recent flags have been declined" banner some room The "some of your recent flags have been declined" message recently got a banner, which makes it stand out  more (which is nice) but it touches the 'Flag' button, which is less nice. Can it have some margin at the bottom (and perhaps less padding?)    Tested in the latest Safari and Firefox on macOS Catalina. Every partially defined isometry can be extended to a isometry I know that the following theorem holds true:  Let $S$ be a subset of $\mathbb R^n$, and let $f:S\to \mathbb R^n$ a map such that $d(p,q)=d(f(p),f(q))$ for every $p,q \in S$ (here $d$ is the usual euclidean distance). Suppose that $0 \in S$ and $f(0)=0$. Then $f$ can be extended to an orthogonal transformation of $\mathbb R^n$.  I have two questions:   Can someone give me a reference of a proof of this theorem? I believe that the previous theorem holds true also if we change $\mathbb R^n$ with $\mathbb C^n$ and "orthogonal" with "unitary", with nearly the same proof. Does it holds true also in the $ \ell^2$ space? With the same proof? In Heaviside-Lorentz units the Maxwell's equations are:  $$\nabla \cdot \vec{E} = \rho $$  $$ \nabla \times \vec{B} - \frac{\partial \vec{E}}{\partial t} = \vec{J}$$ $$ \nabla \times \vec{E} + \frac{\partial \vec{B}}{\partial t} = 0 $$ $$ \nabla \cdot \vec{B} = 0$$  From EM Lagrangian density: $$\mathcal{L} = \frac{-1}{4} F^{\mu \nu}F_{\mu\nu} - J^\mu A_\mu$$   I can derive the first two equations from the variation of the action integral: $S[A] = \int \mathcal{L} \, d^4x$. Is it possible to derive the last two equations from it? MongoDB could not connect local server Second law of Newton for variable mass systems Frequently I see the expression  $$F = \frac{dp}{dt} = \frac{d}{dt}(mv) = \frac{dm}{dt}v + ma,$$ which can be applied to variable mass systems.  But I'm wondering if this derivation is correct, because the second law of Newton is formulated for point masses.   Furthermore if i change the inertial frame of reference, only $v$ on the right side of the formula $F = \frac{dm}{dt}v+ma$ will change, meaning that $F$ would be dependent of the frame of reference, which (according to me) can't be true.   I realize there exists a formula for varying mass systems, that looks quite familiar to this one, but isn't exactly the same, because the $v$ on the right side is there the relative velocity of mass expulsed/accreted. The derivation of that formula is also rather different from this one.   So my question is: is this formula, that I frequently encounter in syllabi and books, correct? Where lies my mistake. I have been working on a Java project for a class for a while now. It is an implementation of a linked list (here called AddressList, containing simple nodes called ListNode). The catch is that everything would have to be done with recursive algorithms. I was able to do everything fine sans one method: public AddressList reverse()      ListNode:    public class ListNode{   public String data;   public ListNode next; }   Right now my reverse function just calls a helper function that takes an argument to allow recursion.  public AddressList reverse(){   return new AddressList(this.reverse(this.head)); }   With my helper function having the signature of private ListNode reverse(ListNode current).  At the moment, I have it working iteratively using a stack, but this is not what the specification requires. I had found an algorithm in C that recursively reversed and converted it to Java code by hand, and it worked, but I had no understanding of it.  Edit: Nevermind, I figured it out in the meantime.  private AddressList reverse(ListNode current, AddressList reversedList){   if(current == null)        return reversedList;   reversedList.addToFront(current.getData());   return this.reverse(current.getNext(), reversedList); }   While I'm here, does anyone see any problems with this route? Linux: coloring bash prompt will break carriage return If I was at point $A$ and I wanted to walk directly to point $B$, I would have to walk half way to point $B$, but before that I would have to walk half way to halfway to halfway to point $B$ and half of that again and so on and so fourth. if I halved this distance an infinite amount of times then there would be an infinite amount of actions I would need to perform in order to cross from $A$ to $B$. Therefore, if each action took any quantity of time at all, then it would take me an infinite amount of time to cross from $A$ to $B$, even if $A$ and $B$ were only a few centimetres apart!   Because I am not infinitely old and I can move, there must be a flaw in this logic. Where is it? I had the following two problems:     Find a counterexample for $f_*(A \cap B) \supseteq f_*(A) \cap f_*(B)$ and $ f_*(A-B) \subseteq f_*(A) -f_*(B).$ Where $f_*(X)$ is the image of $X$ under $f$ for some function $f:A \rightarrow B $ and some subset $X \subseteq A$.   I came with the following answer:  Let $ f: \mathbb{Z} \rightarrow \mathbb{Z} $, where $f: x\mapsto 0$; let $A=\{1,2\}$, and $B=\{3,4\}$.     For $f_*(A \cap B) \supseteq f_*(A) \cap f_*(B)$, $$ f_*(A \cap B) = f_*\{ \varnothing\} = \varnothing \hspace{1cm} \text{and} \hspace{1cm} f_*(A) \cap f_*(B)=\{0\} \cap \{0\} = \{0\}. $$ It follows that $ \varnothing \nsupseteq \{0\} $. For $ f_*(A-B) \subseteq f_*(A) -f_*(B)$, $$f_*(A-B)=f_*(\{1,2\})=\{0\} \hspace{1cm} \text{and} \hspace{1cm} f_*(A) - f_*(B) = \{0\} - \{0\} = \varnothing$$ It follows that $ \{0\}  \nsubseteq \varnothing $.   Now (assuming my answer is correct), let's say I want to find more counterexamples or maybe a more general answer (e.g. all the conditions under which the inclusion fails). Other than by trial and error or just intuition, how would I do that?   I know this is a broad question, so I'm specifically asking for methods or advice on how to build counterexamples in elementary set theory (for example, tips on where to begin or rules that apply in general that may be unobvious). Lightning force:createRecord capture redirect after save Is there a way to use force:createRecord but capture the redirect to the newly created record page that occurs after saving the record? Finally, prevent the redirect from completing?  createRecord : function (component) {     var createRecordEvent = $A.get("e.force:createRecord");     createRecordEvent.setParams({         "entityApiName": "Event__c"     });     createRecordEvent.fire(); } How can we extract specific files from a large tar.gz file? I found  but, when I tried the mentioned command there, I got the error:  $ tar --extract --file={test.tar.gz} {extract11} tar: {test.tar.gz}: Cannot open: No such file or directory tar: Error is not recoverable: exiting now   How do I then extract a file from tar.gz? My coach said that for all positive integers $n$, $n^4+4^n$ is never a prime number.  So we memorized this for future use in math competition.  But I don't understand why is it? Explaining Infinite Sets and The Fault in Our Stars In watching The Fault in Our Stars I could not help but cringe at a line that flew in the face of mathematics and subsequently ruined the movie for me:     "There are infinite numbers between 0 and 1. There's .1 and .12 and .112 and an infinite collection of others. Of course, there is a bigger infinite set of numbers between 0 and 2, or between 0 and a million. Some infinities are bigger than other infinities." - John Green   While walking out of the theater I tried to explain to my friends why there were, in fact, exactly the same amount of numbers between 0 and 1 as 0 and 2, but Cantor and bijective functions are not great learning tools to English majors.  Does anybody have an eloquent or elegant way to enumerate this phenomenon using an example accessible to those not familiar with advanced mathematics? What is the secondary CPU Usage Graph line in the Windows 10 Task Manager I was looking at the task manager in Windows 10 and for the first time noticed a secondary dashed line below the solid? What does this line indicate? @track vs @api (Lightning Web Components) Let's say we have this code for a LWC:  &lt;!-- helloExpressions.html --&gt; &lt;template&gt;     &lt;div class="slds-m-around_medium"&gt;         &lt;lightning-input name='firstName' label="First Name" onchange={handleChange}&gt;&lt;/lightning-input&gt;         &lt;lightning-input name='lastName' label="Last Name" onchange={handleChange}&gt;&lt;/lightning-input&gt;         &lt;p class="slds-m-top_medium"&gt;Uppercased Full Name: {uppercasedFullName}&lt;/p&gt;     &lt;/div&gt; &lt;/template&gt;   and this is the JS file:  // helloExpressions.js import { LightningElement, track } from 'lwc';  export default class HelloExpressions extends LightningElement {     @track firstName = '';     @track lastName = '';      handleChange(event) {         const field = event.target.name;         if (field === 'firstName') {             this.firstName = event.target.value;         } else if (field === 'lastName') {             this.lastName = event.target.value;         }     }      get uppercasedFullName() {         return `${this.firstName} ${this.lastName}`.toUpperCase();     } }   firstName and lastName have been decorated with @track. Now as per the documentation, decorating a property with @track makes it private and reactive, while to mark a property public and reactive, use @api.  So if I just change the decorator to @api for both these variables, it should work. I am referring these from the same component only. But it's not working.  UPDATE: 27th Feb -------------------- Somehow it's working today. I just changed the decorator of the variables to api.  import { LightningElement, api } from 'lwc';  export default class HelloExpressions extends LightningElement {     @api firstName = '';     @api lastName = '';      handleChange(event) {         const field = event.target.name;         if (field === 'firstName') {             this.firstName = event.target.value;         } else if (field === 'lastName') {             this.lastName = event.target.value;         }     }      get uppercasedFullName() {         return `${this.firstName} ${this.lastName}`.toUpperCase();     } }   So it's working. Finding a clear difference between truth and fact I have been starting back in school after a long hiatus.  In one of my classes, a discussion of Truth began.  The problem I have had is that no one seems to have a solid definition between the two.   My earlier training and schooling left me with this definition, and I would like some feedback.  Fact - A point of data that can be directly qualified/quantified through confirmed, standardized measurement.  Truth - A point of data not directly qualified/quantified through confirmed, standardized measurement.  So fact would be that ice cream is cold, as we can place a measurement of the temperature.  Ice cream being tasty would be truth, as it is impossible to accurately measure "tasty".  Please let me know your thoughts. Why is my animation not keeping location and rotation correctly? I am currently 3d modeling a twisty puzzle and trying to animate it. I have the puzzle done but when I try to animate it, it randomly twists and turns the individual objects in different directions before converging back to their original form at the end of the animation.  The screencast of me attempting to animate this is here:   File at the end of the screencast:    This is the original file. Just delete the 2 keyframes that are there:    I did make this with a tutorial. It is by rcpongo and I have very slightly edited his design. All credit goes to him for my design.