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When should you use DateTime and when should you use Time?

It's a common misconception that [William Shakespeare][1] and [Miguel de Cervantes][2] died on the same day in history - so much so that UNESCO named April 23 as [World Book Day because of this fact][3]. However because England hadn't yet adopted [Gregorian Calendar Reform][4] (and wouldn't until [1752][5]) their deaths are actually 10 days apart. Since Ruby's Time class implements a [proleptic Gregorian calendar][6] and has no concept of calendar reform then there's no way to express this. This is where DateTime steps in:

>> shakespeare = DateTime.iso8601('1616-04-23', Date::ENGLAND)
=> Tue, 23 Apr 1616 00:00:00 +0000
>> cervantes = DateTime.iso8601('1616-04-23', Date::ITALY)
=> Sat, 23 Apr 1616 00:00:00 +0000

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def osgb36_to_wgs84(easting, northing)
  # Ellipsoid parameters
  a_airy = 6377563.396      # Semi-major axis (Airy 1830)
  b_airy = 6356256.909      # Semi-minor axis (Airy 1830)
  a_wgs84 = 6378137.0       # Semi-major axis (WGS84)
  b_wgs84 = 6356752.3142    # Semi-minor axis (WGS84)

  # OSGB36 Helmert transformation parameters to WGS84
  tx = 446.448       # Translation along X-axis (meters)
  ty = -125.157      # Translation along Y-axis (meters)

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Generate a Ruby function to convert UK Ordnance Survey OSGB36 co-ordinates to WGS84 latitude and longitude just using pure Ruby and not using a gem.

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Generate a Ruby function to convert UK Ordnance Survey OSGB36 co-ordinates to WGS84 latitude and longitude

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Generate a Ruby on Rails routes file that namespaces a resource called 'Page' under the path '/admin' and restrict it to just the index, edit and update actions.

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Generate a Ruby on Rails controller for a 'Page' resource that is namespaced inside a module called 'Admin'. Implement the index, edit and update actions using path parameter called 'slug' to find the correct model. For the index action sort the pages by the slug column.

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Rails.application.routes.draw do

  get '/(:locale)/products/(:category)/(page/:page).:extension',
        :to => 'products#index',
        :as => :products,
        :constraints => {
          :locale => /[a-z]{2}/,
          :category => /.+?/,
          :page => /\d+/
        },

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module Mapping
  module Utilities
    module NationalGrid
      # All the values and formula are from the Ordnance Survey publication:
      # A guide to coordinate systems in Great Britain
      # https://www.ordnancesurvey.co.uk/documents/resources/guide-coordinate-systems-great-britain.pdf

      # Scale factor on the central meridian for the Transverse Mercator projection
      # https://en.wikipedia.org/wiki/Transverse_Mercator_projection
      F0 = 0.9996012717

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class ActivationsController < ApplicationController

  respond_to :json

  def create
    new_password = params[:user] && params[:user][:password]
    token = params[:confirmation_token]

    if !new_password
      render_errors({"password"=>["can't be blank"]}.to_json)